# Condensed Matter Resnick seminar

### Upcoming Lectures

NanoSQUIDs residing on the apex of a quartz tip (SOT), suitable for scanning probe microscopy with record size, spin sensitivity, and thermal sensitivity are presented[1,2] . We have developed SOT with an effective diameter smaller than 50 nm, spin sensitivity better than a single electron spin and thermal sensitivity better than 1 μK/Hz1/2 . This technique is used to study nanoscale magnetism present in systems such as atomically sharp LaMnO3/SrTiO3 (LMO/STO) heterostructures[3] and to study dissipation mechanism in quantum system such as hBN-encapsulated graphene[2,4] . Magnetic imaging of LMO/STO revealed a superparamagnetic behavior resulting from an electronic phase separation leading to nucleation of metallic ferromagnetic islands in an insulating antiferromagnetic matrix. Thermal imaging of hBN-encapsulated graphene reveals a fascinating atomic-scale dissipation mechanism providing visualization and control of phonon emission from inelastic electron scattering off individual atomic defects[4] , opening the door to direct imaging and spectroscopy of dissipation processes in quantum systems.

[1] D. Vasyukov, Y. Anahory, L. Embon, D. Halbertal, J. Cuppens, L. Neeman, A. Finkler, Y. Segev, Y. Myasoedov, M. L. Rappaport, M. E. Huber, and E. Zeldov, Nature Nanotech. 8, 639 (2013)

[2] D. Halbertal, J. Cuppens, M. Ben Shalom, L. Embon, N. Shadmi, Y. Anahory, H. R. Naren, J. Sarkar, A. Uri, Y. Ronen, Y. Myasoedov, L. S. Levitov, E. Joselevich, A. K. Geim, and E. Zeldov, Nature 539, 407 (2016).

[3] Y. Anahory, L. Embon, C. J. Li, S. Banerjee, A. Meltzer, H. R. Naren, A. Yakovenko, J. Cuppens, Y. Myasoedov, M. L. Rappaport, M. E. Huber, K. Michaeli, T. Venkatesan, and E. Zeldov, Nature Communications 8, 85 (2016)

[4] D. Halbertal, M. Ben Shalom, A. Uri, K. Bagani, A.Y. Meltzer, I. Marcus, Y. Myasoedov, J. Birkbeck, L.S. Levitov, A.K. Geim, and E. Zeldov, Science 358, 1303 (2017).

I shall give theoretical explanations of two surprising experimental observations of universal behaviour in semiconductor systems.

The fist concerns the dependence of photoconductivity $G$ upon light intensity $I$. It is typically found that $G=I^\gamma$. Simple kinetic theory indicates that we should expect $\gamma=1$ or $\gamma=1/2$, but experimentally values close to $\gamma =3/4$ or $\gamma=2/3$ are often observed, with $I$ varying over several decades. I shall present a new explanation for these universal exponents.

The second universality concerns exciton spectroscopy in heterostructures. The linewidth $W$ of the absorption line and the Stokes shift $S$ of the luminescence peak relative to the absorption peak are found to be related by $S/W=0.6$ in most systems for which both values are published. This ratio is independent of the degree of disorder and of the composition of the semiconductors forming the heterostructure, with $W$ varying over two decades. I shall also give a quantitative explanation of this result.

Finally I point out what these two phenomena have in common.

### Previous Lectures

With the rapid development of quantum technologies and the ability to manipulate individual atoms and ion, thermodynamics faces new challenges. The main question is not whether thermodynamics is valid, but whether it is relevant. Does it provide useful predictions on quantities of interest in the microscopic world? By introducing the concept of global passivity we derive an extension of the second law of thermodynamics that can properly handle initial quantum correlations (i.e., entanglement, and quantum discord) between the system and the environment. This extension is very important in nanoscopic setups where the environment may be small and strongly interacting with the system of interest. A second main finding of this framework is a family of additional thermodynamic relations that involve measurable quantities that were so far not constrained by thermodynamics. In particular, we use these relations to set upper and lower bounds on the buildup of system-environment correlation in quantum dephasing scenarios (decoherence). As a second example, we study the evolution of energy covariance between an atom and an optical cavity. Our findings are highly relevant for various modern experimental setups such as ion traps, atoms in an optical cavity or in optical lattices, and more.

Layered materials can be exfoliated to very thin films. In our group we utilize a technique called “mechanical transfer”, which allows stacking of such materials into new types of heterostructures which can involve layers of distinct functionalities. In my talk I will describe this fabrication technique, and demonstrate how we build a new type of device which consists of a layered superconductor (NbSe_{2}), on which we deposit an ultra-thin layer of the semiconductor WSe_{2}. Together, these two materials form a tunneling device, which can be cooled to extremely low temperatures (20 mK) in a dilution cryostat fitted with special filters which allow very sensitive energy spectroscopy. Our tunneling spectra allow tracking the evolution of the superconductor order parameter at the presence of strong magnetic fields, and quantifying its stability. Specifically, the depairing energy scale can be evaluated, and its origin – orbital or spin – identified. Thus, we are able to identify which of the two bands participating in NbSe_{2} superconductivity is associated with this material’s remarkable stability against in-plane magnetic field.

I plan to make a short review of the features of the energy spectrum of carriers in the quantum wells of a gapless semiconductor HgTe, in which, depending on the thickness of the well, the "normal", inverted and semimetallic spectra are realized. I will review the edge, topologically protected states, that should arise in structures with an inverted spectrum (which is realized at a quantum well thickness greater than d_c = 6.3 nm.

In more detail, I will discuss the current state of experimental results on the study of the energy spectrum, the role of edge states in kinetic effects. For a real understanding of any experimental results the reliable knowledge of the energy spectrum is necessary. Theoretically, it has been studied quite well and in detail. However, by the present time, quite a lot of contradictions have accumulated between theory and experiment. Therefore, our main attention will be paid to our experimental studies of the spectrum of the valence band in structures with a well thickness close to d_c and with d> d_с [1,2,3]. It will be shown that interface inversion asymmetry leads to a large spin-orbit splitting, which radically changes the spectrum of the valence band.

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1. G. M. Minkov, A. V. Germanenko, O. E. Rut, A. A. Sherstobitov, M. O. Nestoklon, S. A. Dvoretski, and N. N. Mikhailov, Spin-orbit splitting of valence and conduction bands in HgTe quantum wells near the Dirac point, , Phys. Rev. B 93, 155304 – Published 11 April 2016.

2. G. M. Minkov, V. Ya. Aleshkin, O. E. Rut, A. A. Sherstobitov, A. V. Germanenko, S. A. Dvoretski, and N. N. Mikhailov, Valence band energy spectrum of HgTe quantum wells with an inverted band structure, Phys. Rev. B 96, 035310 (2017) - Published 26 July 2017

3. G.M. Minkov et al, Conductance of a Lateral p–nJunction in TwoDimensional HgTe Structures with an Inverted Spectrum: The Role of Edge States JETP Letters, 2015, Vol. 101, No. 7, pp. 469–473, 2015

Topological insulators have been in the focus of condensed-matter research in recent years. In particular, much effort was dedicated to optically excite and control currents involving the topological surface states. We image the unoccupied bandstructures of a topological insulator as it evolves following an optical excitation, and observe the signature of a photo-induced current. By applying a time-mapping analysis we gain a complete view on the occupied and unoccupied electronic states, and how they are coupled by the optical excitation. This enables us to determine that photocurrents are excited only via the resonant optical transitions, paving the way to optical control of currents in topological insulators.

We study dynamical and steady-state dissipative quantum phase transitions of a driven Bose Hubbard model between an incoherent Mott-like insulating phase and a non-equilibrium superfluid. We highlight the crucial role of pumping scheme and the unique features that emerge in the driven- dissipative case as compared to the well known equilibrium quantum criticality. These results might be relevant for the upcoming generation of circuit QED arrays experiments aiming at realizing Mott Insulator of Polaritons and its transition into a nonequilibrium superfluid.

Generic interacting, disordered and isolated systems were shown to break ergodicity in a dynamical transition, called the many-body localization transition. In this talk I will survey the anomalous dynamical properties of the ergodic phase and will present a phenomenological picture which was proposed to explain them. I will provide evidence which suggest that this picture might not be complete.

Magnetic skyrmions are topologically protected, nanoscale, whorls and hedgehogs of magnetization. Because of their topological properties skyrmions also give rise to novel phenomena such as the topological Hall effect. Low temperature magnetic force microscopy (MFM) provides us with a tool for both imaging and control of skyrmions. Here I will describe recent experiments on multilayer Ir/Fe/Co/Pt stacks which can host Néel (hedgehog) skyrmions. We use MFM to image the magnetic structure in the films as a function of temperature and magnetic field. This allows us to explore the correspondence between the topological Hall effect and the magnetic textures that we image. For the analysis we rely on a new simple model for the magnetic field from a skyrmion.

The spin liquid phase is one of the prominent strongly interacting topological phases of matter whose unambiguous confirmation is yet to be reached despite intensive experimental efforts on numerous candidate materials. The challenge is derived from the difficulty of formulating realistic theoretical models for these materials and interpreting the corresponding experimental data. Here we study a theoretical model with bond-dependent interactions, directly motivated by recent experiments on two-dimensional correlated materials with strong spin-orbit coupling. We show numerical evidence for the existence of an extended family of quantum spin liquids, which are possibly connected to the Kitaev spin liquid state. These results are used to provide an explanation of the scattering continuum seen in neutron scattering on α-RuCl.

We study magnetotransport in a disordered Weyl semimetal taking into

account localization effects. In the vicinity of a Weyl node, a single

chiral Landau level coexists with a number of conventional non-chiral

levels. Disorder scattering mixes these topologically different modes

leading to peculiar localization effects. Similar interplay of topology

and localization occurs at the edge of a two-dimensional topological

insulator and in carbon nanotubes. We develop a general theory

describing transport phenomena in all these cases. Our theory yields

conductance, shot noise power, and full counting statistics of the

charge transfer. In the case of a Weyl semimetal, we find that

localization is greatly enhanced in a strong magnetic field with the

typical localization length scaling as 1/B. This situation is typical

for all topological conductors with broken time-reversal symmetry.

Systems with preserved time-reversal symmetry (e.g., carbon nanotubes),

sustain at most one topologically protected channel. For this case, we

derive exact distribution function of transmission probabilities based

on the mapping to a certain random-matrix model.

Over the past 5 years or so, superconductivity has been observed in a number of different materials with an extremely low density of charge carriers. Some of these are even among the most dilute metals that exist, such as SrTiO3 and bismuth. In this limit, the screening of the Coulomb repulsion is poor, and moreover, the conventional phonon mechanism for superconductivity is completely irrelevant. This raises the question: how can these materials be superconducting? I will propose two different mechanisms for superconductivity in low-density metals, based on dynamically screened Coulomb interactions and fluctuations near a structural quantum critical point. I will further discuss the prospects of these mechanisms for topological superconductivity and superconductivity in two-dimensional materials.

The Josephson effect in conventional superconductors has led to a variety of extensions and applications from SQUID magnetometers to pairing symmetry detection using planar junctions. It is therefore interesting to extend the discussion to topological Josephson junctions where Majorana fermions, and not just Cooper pairs, can tunnel through the junction. In this talk I will consider a setup made of a ring of topological superconducting wires separated by Junctions and coupled to a quantum dot. The coupling to the quantum dot serves as a knob which tunes the periodicity of the current in the junction as a function of external flux. The periodicity can change from one flux quantum (h/2e), expected from a conventional junction, to that of a topological junction, h/e. This tuning ability can distinguish between a topological junction and a dirty non-topological junction. I will also discuss phase slips and the suppression of 2pi phase slips in topological Josephson junctions.

Bilayer graphene subjected to magnetic and electric fields exhibits a plethora of phases with radically distinct behaviors. Most prominently, the \nu=0** **quantum Hall state which develops at zero doping manifest a rich phase diagram marked by changes in the electrical conductance, and is tunable by either of the external fields. This behavior is attributed to the variety of many-body states with broken symmetry, which can form due to the multi-component nature of the discrete degrees of freedom (spin, valley and orbital isospin). In particular, in the presence of a perpendicular electric field D, at least two distinct insulating phases are identified: a canted antiferromagnet (CAF) at low D, and a fully layer polarized (FLP) phase at low D. However, at intermediate values of D and the magnetic field B, a finite conductance is developed, potentially indicating the formation of novel intermediate phases. I present a theoretical study motivated by these observations, which accounts for the interplay between lattice-scale interactions, inherently anisotropic in the spin-valley-orbital manifold, and a (formerly overlooked) trigonal warping effect in the electronic band-structure. Employing a Hartree-Fock calculation, we find several competing many-body states characterized by unusual spin-valley entangled correlations, which are promising candidates for the ground-state at intermediate fields. Most interestingly, we find a regime of parameters where the emergent intermediate phase is characterized by a simultaneous breaking of two distinct U(1) symmetries. I further discuss the implications on transport properties; most remarkably, the emergence of high conductance is a possible signature of robust collective edge modes associated with textures in the spin/valley manifold, which are topological in nature.

The anomalous Hall effect arises in systems with both spin-orbit coupling and magnetization.

We study the minimal model of the anomalous Hall effect based on the massive Dirac Hamiltonian and consider two

limiting cases of weak (Gaussian) and strong (Poisson) impurities.

The standard diagrammatic approach to the problem is limited to computation of ladder diagrams.

We demonstrate that this is insufficient in the case of Gaussian disorder. An important additional contribution comes from

scattering on pairs of closely located defects and essentially modifies previously obtained results for anomalous Hall conductivity.

n the case of Poisson disorder, we go beyond semiclassical limit and calculate weak

localization corrections. Unlike the case of ordinary Hall effect, we identify a finite quantum correction to anomalous Hall resistivity.

Depending on the structure of impurities, this correction can have any sign and interpolates smoothly between universal orthogonal

(localization) and symplectic (antilocalization) limits.

Recent experiments have provided mounting evidence for the existence of Majorana

bound states (MBSs) in condensed-matter systems. Until the long-term goal of braiding MBSs is

achieved, one is prompted to ask: what is the next step in the study of topological

superconductivity and MBSs? In my talk I will discuss two topics relating to this question. In the

first part I will examine the possibility of, not only detecting the Majoranas, but also witnessing

some of their exotic properties. In particular their non-local nature, or in other words, the fact that

the MBS is half a fermion whose occupation is encoded in a nonlocal way. I will show that current

cross correlations in a T-junction with a single MBS exhibit universal features, related to the

Majorana nonlocality. This will be contrasted with the case of an accidental low-energy Andreev

bound state. In the second part I will discuss the possibility of realizing a different topological

phase hosting MBSs in currently available experimental platforms. This will be a topological

superconducting phase which is protected by time-reversal symmetry, and which is characterized

by having a Kramers’ pair of MBSs at each end. As I will discuss, repulsive interactions are a

necessary ingredient for the realization of this phase. I will present a mechanism, based on the

interplay between repulsive interactions and proximity to a conventional superconductor, which

drives the system into the topological phase. The effect of interactions is studied analytically using

both a mean-field approach and the renormalization group. We corroborate our conclusions

numerically using DMRG.

The current that flows in a ring can be a signature of fundamental and topological properties of quantum states of charge-carrying particles. Applying a magnetic flux through a ring creates a phase gradient, in response to which a current flows, creating magnetic fields that we measure with a scanning SQUID microscope. I will take you on a tour of currents and phases in common and exotic quantum materials. Gold rings are normal metals with finite resistance, but remarkably, they carry persistent currents whose sign and magnitude confirm the quantum behavior of disordered metals. Aluminum rings superconduct at low temperatures, and are an ideal model system to study superconducting fluctuations. The strong agreement of theory and experiment in conventional metals and superconductors sets the stage to study superconducting rings interrupted by a single Josephson junction. This geometry allows us to measure a fundamental and informative property of the junction, called the current-phase relation. In junctions made of topological materials, the current could theoretically be 4pi-periodic rather than 2pi-periodic as a function of the phase winding in the ring. I will report on progress towards this smoking-gun signature for Majorana modes.

N/A

I will compare the effects of quantum and thermal fluctuations in a spin chain by calculating the probability distribution for spin fluctuations in a segment. The calculation will use the concept of an "entanglement Hamiltonian." The entanglement Hamiltonian can be used to identify topological phases, but I will show that it is helpful for long-wavelength correlations as well as topological ones. The entanglement Hamiltonian is an imaginary system that describes the correlations of the ground state. It cannot be measureddirectly, but it is related to the statistics of the fluctuations, so measuring the spin fluctuations of the atoms on the sites of an optical lattice is an indirect way of measuring the entanglement Hamiltonian.

In this talk, I will address the question of the existence of gapless topological superconducting phases in one dimension. I will present a general approach to treat charge-conserving one-dimensional systems with pairing interactions, and argue that in presence of symmetries the notion of a topological phase can be well defined although the system is gapless. I will demonstrate our approach on systems with time-reversal symmetry and on systems with SO(3) symmetry, where a gapless analogue of the Haldane phase in spin-1 chains can be realized.

Jun Ye

JILA, National Institute of Standards and Technology and University of Colorado, Boulder, Colorado 80309-0440, USA

Engineered spin–orbit coupling (SOC) in cold atom systems can shed light to synthetic materials and complex condensed matter phenomena. We demonstrate that SOC between fermions can be engineered to occur naturally in an optical lattice clock. SOC is both generated and probed using a direct ultra-narrow optical clock transition between two electronic orbital states in ^{87}Sr atoms. We use clock spectroscopy to prepare lattice band populations, internal electronic states and quasi-momenta, and to produce spin–orbit-coupled dynamics. The exceptionally long lifetime of the excited clock state eliminates decoherence and atom loss from spontaneous emission at all relevant experimental timescales, allowing subsequent momentum- and spin-resolved in-situ probing of the SOC band structure and eigenstates. We use these capabilities to study Bloch oscillations, spin–momentum locking and Van Hove singularities in the transition density of states. Furthermore, many-body correlations arising from the interplay of interactions and SOC have been observed recently.

E-mail: Ye@JILA.colorado.edu

We study the density of states (DOS) and the transition temperature Tc in a dirty superconducting film with rare classical magnetic impurities of an arbitrary strength described by the Poissonian statistics. We take into account that the potential disorder is a source for mesoscopic fluctuations of the local DOS, and, consequently, for the effective strength of magnetic impurities. We find that these mesoscopic fluctuations result in a non-zero DOS for all energies in the region of the phase diagram where without this effect the DOS is zero within the standard mean-field theory. This mechanism can be more efficient in filling the mean-field superconducting gap than rare fluctuations of the potential disorder (instantons). Depending on the magnetic impurity strength, the suppression of Tc by spin-flip scattering can be faster or slower than in the standard mean-field theory.

Energy dissipation is a fundamental process governing the dynamics of physical systems. In condensed matter physics, in particular, scattering mechanisms, loss of quantum information, or breakdown of topological protection are deeply rooted in the intricate details of how and where the dissipation occurs. Despite its vital importance, direct imaging of dissipation in quantum systems is currently impossible because the existing thermal imaging methods lack the necessary sensitivity and are unsuitable for low temperature operation.

We developed a scanning nanoSQUID with sub 50 nm diameter that resides at the apex of a sharp pipette [1] that can act simultaneously as nanomagnetometer with single spin sensitivity and as nanothermometer providing cryogenic thermal imaging with four orders of magnitude improved thermal sensitivity of below 1 µK/Hz^{1/2} [2]. The non-contact non-invasive thermometry allows thermal imaging of very low nanoscale energy dissipation down to the fundamental Landauer limit of 40 fW for continuous readout of a single qubit at 1 GHz at 4.2 K. These advances enable observation of changes in dissipation due to single electron charging of individual quantum dots in carbon nanotubes. Our thermal imaging study of hBN encapsulated graphene reveals a fascinating dissipation mechanism due to resonant localized states at the edges of graphene providing the first visualization of inelastic electron scattering mechanism on the nanoscale, opening the door to direct imaging of microscopic dissipation processes in quantum matter.

[1] Vasyukov *et al*., Nature Nanotech. **8**, 639 (2013).

[2] Halbertal *et al*., Nature **539**, 407 (2016).

Spectroscopy is a powerful tool to probe matter. By measuring the spectrum of excitations, one can reveal the symmetries and topological properties of a physical system. Mesoscopic devices offer a unique possibility to both engineer and investigate novel excitations. Unfortunately, conventional spectroscopy techniques suffer several drawbacks for coupling radiation to mesoscopic systems and detecting their small absorption signals.

We propose an on-chip, Josephson-junction based spectrometer which surpasses state-of-the-art instruments and is ideally suited for probing elementary excitations in mesoscopic systems. It has a SQUID-based design providing uniform wideband coupling from 2-2000 GHz, low background noise, high sensitivity, and narrow linewidth. We describe the operating principle and design of the spectrometer, show preliminary results demonstrating proof-of-concept, and outline experiments which exploit the spectrometer to investigate unconventional Andreev states.

I will present two projects, based on the use of coupled superconducting resonators, to observe quantum effects:

1. Multiple bosons undergoing coherent evolution in a coupled network of sites constitute a so-called quantum walk system. The simplest example of such a two-particle interference is the celebrated Hong-Ou-Mandel interference. When scaling to larger boson numbers, simulating the exact distribution of bosons has been shown, under reasonable assumptions, to be exponentially hard. We analyze the feasibility and expected performance of a globally connected superconducting resonator based quantum walk system, using the known characteristics of state-of-the-art components. We simulate the sensitivity of such a system to decay processes and to perturbations and compare with coherent input states.

2. Atomic sized two-level systems (TLSs) in dielectrics are known as a major source of loss in superconducting devices, particularly due to frequency noise. However, the induced frequency shifts on the devices, even by far off-resonance TLSs, is often suppressed by symmetry when standard single-tone spectroscopy is used. We introduce a two-tone spectroscopy on the normal modes of a pair of coupled superconducting coplanar waveguide resonators to uncover this effect by asymmetric saturation. Together with an appropriate generalized saturation model this enables us to extract the average single-photon Rabi frequency of dominant TLSs to be Ω_{0}/2π≈79 kHz. At high photon numbers we observe an enhanced sensitivity to nonlinear kinetic inductance when using the two-tone method and estimate the value of the Kerr coefficient as K/2π≈−1×10^{−4}Hz/photon. Furthermore, the life-time of each resonance can be controlled (increased) by pumping of the other mode as demonstrated both experimentally and theoretically.

Periodically driven quantum systems, such as semiconductors subject to light and cold atoms in optical lattices, provide a novel and versatile platform for realizing topological phenomena. Among these are analogs of topological insulators and superconductors, attainable in static systems. However, some of these phenomena are unique to the periodically driven case. I will describe how the interplay between periodic driving, disorder, and interactions gives rise to new steady states exhibiting robust topological phenomena, with no analogues in static systems. Specifically, I will show that disordered two dimensional driven systems admit an “anomalous" phase with chiral edge states that coexist with a fully localized bulk. This phase serves as a basis for new far-from-equilibrium quantized transport phenomena. Specifically, I will discuss the quantization of magnetization and two terminal currents in this anomalous phase.

**Experimental probing of quantum criticality at the Superconductor-Insulator Quantum Phase Transition**

The superconductor-insulator transition (SIT) is a prototype of a quantum phase transition which is very versatile experimentally: varying a non-thermal tuning parameter such as disorder, thickness, composition, magnetic field or gate-voltage causes the system to switch from a superconductor to an insulator at zero temperature.

Unlike their classic counterparts, quantum phase transitions are governed by quantum rather than thermal fluctuations at low temperatures. The direct experimental study of such fluctuations close to the SIT is rather challenging. So far research has mainly concentrated on dc resistivity based measurements such as transport and magnetoresistance and on global and local tunneling spectroscopy. These cannot provide explicit information on the critical behavior through the transition.

In my talk I will describe two experimental efforts designed to measure signatures of quantum fluctuations close to quantum criticality. The first experiment utilizes a unique, highly sensitive, setup to measure the specific heat of ultrathin Pb films through the SIT. The specific heat is found to increase considerably as the sample is pushed towards the SIT thus signaling quantum criticality. The second experiment is a scanning squid measurement able to probe local susceptibility in TiNbN films close to the quantum transition. These studies reveal electronic superconducting granularity which fluctuates in time and space at temperatures well below Tc. The temperature regime of these fluctuations grows as the SIT is approached indicating their quantum nature.

I will discuss the significance of these results and their contribution to understanding the electronic processes in the vicinity of the quantum phase transition.

Precise timekeeping is critical to metrology, forming the basis by which standards of time, length and fundamental constants are determined. Stable clocks are particularly valuable in spectroscopy as they define the ultimate frequency precision that can be reached. In quantum metrology, where the phase of a qubit is used to detect external fields, the clock stability is defined by the qubit coherence time, and therefore determines the spectral linewidth and frequency precision. I will present a demonstration of a quantum sensing protocol for oscillating fields where the spectral precision goes beyond the sensor coherence time and is limited by the stability of a classical clock. Using this technique, we observe a precision in frequency estimation scaling as 1/T^{3/2} for classical fields. The narrow linewidth magnetometer based on single quantum coherent spins in diamond is used to sense magnetic fields with an intrinsic frequency resolution of 607µHz, 8 orders of magnitude narrower than the qubit coherence time.

Transition metal oxides (TMOs) are complex electronic systems which exhibit a multitude of collective phenomena. Two archetypal examples are VO_{2} and NdNiO_{3}, which undergo a metal-insulator phase-transition (MIT), the origin of which is still under debate.

We have discovered a new kind of memory effect in both systems, manifest through an increase of resistance at a specific temperature, which is set by reversing the temperature-ramp from heating to cooling during the MIT, thus we call it ‘Ramp Reversal Memory’.

The characteristics of this memory effect do not coincide with any previously reported history or memory effects in similar systems. From a broad range of experimental features, supported by theoretical modelling, we claim that the main ingredients for the effect to arise are the spatial phase-separation of metallic and insulating regions during the MIT and the coupling of lattice strain to the local critical temperature of the phase transition. We predict that similar ramp-reversal effects exist also in other systems.

Search engines, e-mail, watch-on-demand websites, cyber-security and smartphones are examples of how information technologies have changed our lives in the past decade. However, the growing usage of these technologies has arrived with a cost—a sharp increase in global electrical-energy consumption. Likewise, the inability to manage heat has already become crucial for mobile-phones. Hence, novel materials that will replace the existing technologies are being sought continuously. Superconductors and ferroelectrics are functional solid-state systems that exhibit unique collective electron behavior, which renders these systems for energy-efficient nano switching devices. Nevertheless, to date the understanding and controllability of the emergence of collective-electron behavior in these materials, which is also at the nanoscale, has remained elusive to us, hindering the realization of their great technological potential.

We developed and utilized methods to expose the collective electron behavior in superconductors and ferroelectrics at the deep submicron scale. For instance, using advanced atomic force microscopy (AFM) and transition electron microscopy (TEM) techniques we have tailored the multiscale ferroelectric behavior (Fig. 1). Likewise, using advanced nano-fabrication designs, we demonstrated how the superconducting behavior can be controlled at the nanoscale. Thanks to the strong correlation between electron collectiveness and functionality in these materials, not only have we illuminated the origin of collective electron interactions in solid-state systems, but we also facilitated novel technologies, ranging from single-photon detectors to quantum switching devices.

[1] Bar Lev and Reichman, Phys. Rev. B 89, 220201(R) (2014).

Practical quantum information processing relies on the ability to protect qubits against errors. This is often achieved by encoding every qubit in multiple two-level systems (“physical qubits”), thus forming a redundantly encoded “logical qubit”. However, implementing gates between such logical qubits requires a large number of operations between pairs of physical qubits.

In this talk, I will present a scheme for an entangling gate between two redundantly encoded logical qubits, and its recent experimental realization. The scheme relies on an alternative approach for realizing logical qubits, which uses the multilevel structure of a single cavity, instead of multiple two-level systems. A single ancillary transmon is used to induce nonlinear coupling between two cavities, thereby generating an effective interaction between the photonic states. The gate is controlled using parametric pumping on the transmon, resulting in an entangling rate between the cavities that is three orders of magnitude larger than the cavity decoherence rate and parasitic interactions. We characterize the gate by full quantum process tomography, and measure a reduction in fidelity per gate application as low as ~1%, on par with state-of-the-art gates between two-level physical qubits. These results demonstrate the potential of cavity-encoded logical qubits beyond the robust storage of quantum information, and open a route towards their use in larger quantum networks.

Photonic cluster states are a resource for quantum computation based solely on single-photon measurements. We use semiconductor quantum dots to deterministically generate long strings of polarization-entangled photons in a cluster state by periodic timed excitation of a precessing matter qubit. In each period, an entangled photon is added to the cluster state formed by the matter qubit and the previously emitted photons. In our prototype device, the qubit is the confined dark exciton, and it produces strings of hundreds of photons in which the entanglement persists over five sequential photons.

*Work done in collaboration with Ido Schwartz, Dan Cogan, Emma Schmidgall, Yaroslav Don, Liron Gantz, Oded Kenneth, and Netanel Lindner [Schwartz et al Science **354**, 434, (2016)].

We have previously demonstrated that as the 1D confinement potential is weakened the electron wavefunctions relax in the second dimension and can form a two-row system, we now show that a zig-zag formation can be observed in electron focusing experiments. In a similar way we have investigated the dynamics of a strongly confined 1D electron gas and will show that a spin separation occurs. We present direct evidence that this spontaneous spin polarization is responsible for the 0.7 anomaly and can rule out other explanations.

I will open my talk by explaining the fundamental concept of parametric resonance and giving examples of some practical application (Paul traps, Kapitza pendulum). I will then clarify why the existence of this phenomenon in many-body systems is still debated. Although it is believed that large systems cannot display true parametric resonances, I will overview some exceptions to this general rule. In the last part of the talk, I will describe some new results on the dynamics of periodically-driven many-body quantum systems.

**Synopsis : I will argue that quantum mechanics endows us with resources that may boost thermodynamic performance: heat-machine power, cooling speed or work, but the basic thermodynamic bounds are still adhered to.**

The debated rapport between thermodynamics and quantum mechanics will be addressed in the framework of the theory of periodically driven/controlled quantum thermodynamic machines. The basic models studied by us are a two-level system (TLS) or a harmonic oscillator, whose energy is periodically modulated while the system is coupled to two distinct thermal baths. When the modulation interval is short compared to the bath memory time, the system–bath correlations are affected, thereby causing cooling or heating of the TLS, depending on the interval [1,2]. This setup constitutes the simplest (minimal) quantum heat machine (QHM) that may operate as either an engine or a refrigerator, depending on the modulation/driving rate [3]. It is used by us to scrutinize basic thermodynamic principles in the quantum domain:

- It is possible to
**surpass the Carnot bound**when the driving is done by a quantum device (piston) in an appropriate state [4-6]. However, such enhanced efficiency does not mean that quantum effects invalidate the Carnot bound: their classical analog is a non-thermal bath whose temperature is controlled by its state. By contrast, engines powered by non-thermal (e.g. squeezed) baths may cease to be heat machines and act instead as devices exchanging work rather than heat with the baths, so that the Carnot bound is inapplicable to such devices [7]. - An extension of the TLS model of quantum heat machines to multiple entangled TLS shows that the
**power output can be boosted by the quantum cooperativity**of these systems, but the efficiency is still bounded by Carnot [6] . - The refrigeration effected by such QHMs
**persists as the temperature approaches absolute zero**for certain quantized baths, e.g., magnons, thus**challenging the Third Law**(Nernst's unattainability principle) [2].

Thus, we may conclude that quantum machines powered by thermal and non-thermal baths may benefit from hitherto unexploited quantum resources, but they still comply with traditional thermodynamic rules, possibly with the exception of the Third Law.

[1] N.Erez et al., Nature 452, 724 (2008).

[2] M. Kolar et al. PRL 109, 090601 (2012).

[3] D. Gelbwaser-Klimovsky et al. PRE 87, 012140 (2013).

One of the major and long-standing challenges of oxide 2DEGs is still to understand how to enhance the electron mobility. The mobility is still orders of magnitude lower than that of the conventional semiconductors and with the current fabrication method we still cannot fully control the charge at the interface. Here, I will present the recent activities of our group in this area where we try to push the mobility to record high values, i.e. the usage of the so-called modulation-doping technique has significantly increased the carrier mobility to mobility of 70.000 cm2/Vs and realization of quantum Hall effect in these films. These findings pave the way for studies of mesoscopic physics with complex oxides and design of high-mobility all-oxide electronic devices.

Zero-resistance in superconductors is protected at finite temperatures by the global phase coherence, which by virtue of the uncertainty principle guarantees the dissipationless flow of Cooper pairs. In two-dimensional critically disordered films dual superinsulating state can form. In superinsulators coherent fluctuations of phase localize Cooper pairs leading to infinite-resistance at finite temperatures. I will present an experimental observation of the magnetic field-driven superconductor-superinsulator transition in disordered thin NbTiN films. Appearance of the superinsulator is detected by the abrupt upturn from the Arrhenius-type temperature dependence of the resistance, evidencing formation of the zero-conducting state at finite temperature. At relatively low magnetic fields we have found the critical divergent behavior of the resistance characteristic to charge Berezinskii–Kosterlitz–Thouless (BKT) transition, which is dual to the vortex BKT transition in superconducting state.

This seminar has been cancelled in order not to overlap with Assa's birthday conference:

http://phsites.technion.ac.il/ieqm2016/program/

Using exact diagonalization for non-interacting systems and density matrix renormalization group for interacting systems we show that Li and Haldane’s conjecture [1] on the correspondence between the low-lying many-particle excitation spectrum and the entanglement spectrum holds for disordered ballistic one-dimensional many-particle systems. We observe and explain the presence of an unexpected shell structure in the excitation spectrum [2]. The low-lying shells are robust and survive even for strong electron-electron interactions.

[1] Li H. and Haldane F. D. M., *Phys. Rev. Lett.*, **101**(2008) 010504.

[2] S. Leiman, A. Eisenbach and R. Berkovits, EPL, 112 (2015).

**One of the defining properties of electrons is their mutual Coulombic repulsion. In solids, however, this basic property may change. A famous example is that of superconductors, where coupling to lattice vibrations makes electrons attract each other and leads to the formation of bound pairs. But what if all degrees of freedom are electronic? Is it still possible to make electrons attractive via their repulsion from other electrons? Such a mechanism, termed ‘excitonic’, was proposed fifty years ago by W. A. Little**,** aiming to achieve stronger and more exotic superconductivity****, yet despite many experimental efforts, direct evidence for such ‘excitonic’ attraction is still lacking****. Here, we demonstrate this unique attraction by constructing, from the bottom up, the fundamental building block**** of this mechanism. Our experiments are based on quantum devices made from pristine carbon nanotubes, combined with cryogenic precision manipulation. Using this platform we demonstrate that two electrons can be made to attract using an independent electronic system as the binding glue. Owing to its large tunability, our system offers crucial insights into the underlying physics, such as the dependence of the emergent attraction on the underlying repulsion and the origin of the pairing energy. We also demonstrate transport signatures of ‘excitonic’ pairing. This experimental demonstration of ‘excitonic’ pairing paves the way for the design of exotic states of matter.**

**Probing Odd-Triplet Contributions to the Proximity Effect by Scanning Tunneling Spectroscopy**

S. Diesch^{1}, M. Wolz^{1}, P. Machon^{1}, C. Sürgers^{2}, W. Belzig^{1}, A. Di Bernardo^{3}, Y. Gu^{3}, J. Linder^{4}, M. G. Blamire^{3}, J. W. A. Robinson^{3}, E. Scheer^{1}

^{1}Department of Physics, University of Konstanz, 78457 Konstanz, Germany

^{2}Physical Institute, Karlsruhe Institute of Technology, 76049 Karlsruhe, Germany

^{3}Department of Material Science and Metallurgy, University of Cambridge, 27 Charles Babbage Road, Cambridge CB3 0FS, United Kingdom

^{4}Physics Institute, Norwegian Technical University, 7491 Trondheim, Norway

**Abstract.** In this talk we will address the superconducting proximity effect between a superconductor (S) and a normal metal (N) linked by a spin-active interface. With the help of a low-temperature scanning tunneling microscope [1,2] we study the local density of states of trilayer systems. The first example consists of aluminum (S), the ferromagnetic insulator (FI) EuS, and the noble metal silver (N) for varying thickness of the FI. In several recent studies it has been shown that EuS acts as ferromagnetic insulator with well-defined magnetic properties down to very low thicknesses [3]. For very thin FI with *d*_{FI} = 2 nm we find a strong enhancement of the induced minigap at the normal side. For intermediate thickness we observe pronounced subgap structures that vary from contact to contact. For *d*_{FI} = 10 nm the spectra are in agreement with the diffusive theory for S/N structures (without FI) as confirmed in earlier studies [2]. We discuss our findings in the light of recent theories of odd-triplet contributions created by the spin-active interface [4,5,6].

The second example uses the ferromagnetic metal (FM) Ho between niobium (S) and gold (N) [7]. These measurements reveal pronounced changes to the Nb sub-gap superconducting density of states on driving the Ho through a metamagnetic transition from a helical antiferromagnetic to a homogeneous ferromagnetic state for which a conventional BCS gap is recovered. The results directly verify odd frequency spin-triplet superconductivity at superconductor / inhomogeneous magnet interfaces [8].

References

[1] C. Debuschewitz, F. Münstermann, V. Kunej, E. Scheer

*A compact and versatile scanning tunnelling microscope with high energy resolution for use in a ^{3}He Cryostat, *J. Low Temp. Phys.

**147**, 525 (2007)

[2] M. Wolz, C. Debuschewitz, W. Belzig, E. Scheer

*Evidence for attractive pair interaction in diffusive gold films deduced from studies of the superconducting proximity effect with aluminium, *submitted

[3] J. Linder, A. Sudbø, T. Yokoyama, R. Grein, M. Eschrig, Phys. Rev. B **81**, 214505 (2010)

[4] B. Li, N. Roschewsky, B. A. Assaf, M. Eich, M. Epstein-Martin, D. Heiman, M. Münzenberg, and J. S. Moodera, Phys. Rev. Lett. **110**, 09700 (2013)

[5] A. Cottet, W. Belzig, Phys. Rev. B **72**, 180503R (2005);

[6] P. Machon, W. Belzig, in preparation

[7] W. A. Robinson, J. D. S. Witt, M. G. Blamire, Science **329**, 59 (2010).

[8] A. Di Bernardo, S. Diesch, Y. Gu, J. Linder, M.G. Blamire, E. Scheer, J. W. A. Robinson, Nature Comm. **6**, 8053 (2015)

Glass is a unique state of matter which appears in many physical systems, including amorphous SiO_{2} (window glass), spin glass, polymer glass, etc., all characterized by the lack of internal order and extremely slow dynamics. The electron glass is a newcomer to this field. In these systems strong Coulomb interactions between localized electrons result in a slow relaxation of the conductance towards equilibrium.

In my talk I will present experimental results obtained on discontinuous metallic films which were fabricated at cryogenic temperatures, below the glass temperature. The conductance dynamics in these samples depend not only on the ambient temperature, but also on the maximal temperature they were exposed to, Tmax. Based on a model of hopping between metastable states, I will claim that this dependence on Tmax may provide insight into the dynamics of many glassy systems.

Superconducting qubits based on Josephson junctions are a promising platform for quantum computation, reaching quality factors of over one million. On one hand, such high quality factors enable the implementation of quantum error correction; on the other, they make possible the investigation of decoherence mechanisms with high accuracy. An intrinsic decoherence process originates from the coupling between the qubit degree of freedom and the quasiparticles that tunnel across Josephson junctions. In this talk I will review briefly the general theory of quasiparticle effects, valid both for equilibrium and non-equilibrium quasiparticles, and discuss recent experiments with transmon and fluxonium qubits. In a transmon, tunneling of a single quasiparticle is associated with a change in parity; I will compare the theory of the parity-switching rate with recent measurements and comment on the implications for the dephasing rate. In qubits that can be tuned by magnetic flux, such as the fluxonium, the quasiparticle-induced decoherence rate depends on the flux; this provides a way to differentiate quasiparticle tunneling from other sources of decoherence. Taking advantage of this flux dependence, we have recently solved a 40-year-old puzzle in the physics of Josephson junctions.

Superconducting qubits based on Josephson junctions are a promising platform for quantum computation,

reaching quality factors of over one million.

On one hand, such high quality factors enable the implementation of quantum error correction; on the other, they make possible the investigation of decoherence mechanisms with high accuracy. An intrinsic decoherence process originates from the coupling between the qubit degree of freedom and the quasiparticles that tunnel across Josephson junctions. In this talk I will review briefly the general theory of quasiparticle effects, valid bothfor equilibrium and non-equilibrium quasiparticles, and discuss recent experiments with transmon and fluxonium qubits.

In a transmon, tunneling of a single quasiparticle is associated with a change in parity; I will compare the theory of the parity-switching rate with recent measurements and comment on the implications for the dephasing rate. In qubits that can be tuned by magnetic flux, such as the fluxonium, the quasiparticle-induced decoherence rate depends on the flux; this provides a way to differentiate quasiparticle tunneling from other sources of decoherence. Taking advantage of this flux dependence, we have recently solved a 40-year-old puzzle in the physics of Josephson junctions.

**The talk will have three parts, discussing electronic transport in three different one-dimensional systems: (i) A junction of three interacting quantum wires has many interesting and distinct transport properties compared to a single quantum wire with a scattering centre. Classification of Y-junctions and interesting results on conductance of Y-junctions will be mainly discussed. (ii)-Periodically driven one-dimensional quantum wires, can pump charge. Results on charge pumping in closed and open systems will be contrasted. Further, pumping on the edge of quantum spin Hall insulators will be discussed. (iii) A recent proposal to enhance crossed Andreev reflection in “normal metal - superconductor - normal metal” will be discussed****. **

**References: **

**A. Soori and D. Sen, EPL 93, 57007 (2011) & A. Soori and D. Sen, PRB 84, 035422 (2011).****A. Soori and D. Sen, Phys. Rev. B 82, 115432 (2010) & A. Soori, S. Das, and S. Rao, Phys. Rev. B 86, 125312 (2012).****A. Soori and S Mukerjee, arxiv: 1603.00363 (2016).**

Ultrafast laser pulses have been used to manipulate complex quantum materials and to induce dynamical phase transitions. One of the most striking examples is the transient enhancement of superconductivity in several classes of materials upon irradiating them with high intensity pulses of terahertz light. Motivated by these experiments we analyze the Cooper pairing instabilities in non-equilibrium electron-phonon systems and demonstrate that the light induced non-equilibrium state of phonons results in an enhancement of Cooper pairing. This opens the possibility of transient light induced superconductivity at temperatures that are considerably higher than the equilibrium transition temperature

They tried to kill us. We survived. Let's eat!

ESRSTM (electron spin resonance scanning tunneling microscopy )is a technique capable of detecting single spins by recording the power spectral density at the Larmor frequency - in the tunneling current. Description of previous results will be provided. Recently a Si(111)7 × 7 surface exposed to 0.1 L of O_2 and the carbonized Si(111) surface are investigated by ESR-STM using frequency sweeps and magnetic field sweeps. Only after oxidizing the clean Si(111)7 × 7 or by using the carbonized Si(111), spatially averaged ESR-STM spectra exhibit several peaks and dips around the frequencies corresponding to g = 2. The energy difference between these features is close to the known hyperfine splitting of A ≅ 9 MHz for vacancies in SiC interacting with next-nearest neighbor ^29 Si. The final proof that the hyperfine spectrum is indeed observed, is the observation of the nuclear Zeeman transition of a single nuclear spin that were observed by an ENDOR type experiment. The results of this experiment reveals the gyromagnetic ratio of 29^Si nuclei. ESRSTM was observed also on Cu atoms. The ENDOR experiment will be carried out to detect the gyromagnetic ratios of the two types Cu nuclei. These results were performed in frequency domain. In this mode the technique is time consuming as the different frequency components are detected one after the other. In time domain, the acquisition is orders of magnitude faster. Results on adsorbed Tempo molecules will be presented. These results display the whole spectrum from 0-0.75GHz. The results reveal the expected Larmor frequency components of Tempo (f1) and additional higher frequency components that are interpreted as tip spin centers (f2). In addition strong peaks appear at a frequency (f1-f2)/2 which may point to a possible mechanism of interference between electrons that are propagating through tip and sample spin centers, respectively.

Perovskite oxides of transition metals offer scientists and engineers a theme park of new physics, with complex structure-property relations and a wide scope of useful phenomena. Advances in epitaxial growth techniques bring unprecedented possibilities of atomic engineering of these oxides and their interfaces, with exciting prospects of unravelling their underlying physics and harnessing it towards useful applications. However, fundamental material challenges inhibit the introduction of these materials onto semiconductors and thus into the microelectronics technology.

The potential of the oxides’ functionalities to evolve out of the labs and into technology has received a considerable boost with the pioneering of epitaxial growth approaches for perovskites directly on semiconductors. This combination opens a route to bridge between oxide functionalities and microelectronics. Moreover, interface engineering of oxides on semiconductors can lead to new functionalities, made possible by the coupling between the dissimilar materials.

The formation of a 2 dimensional electron gas (2DEG) is a prominent example of an unexpected phenomenon occurring at the interface of two insulating oxides, with complex underlying physics and potential for technological applications. We demonstrate the integration of high carrier density oxide 2DEGs on silicon, which brings the useful properties of 2DEGs closer to application in microelectronics. In order to put this claim to the test, we assess the performance of oxide 2DEGs on silicon as potential channels.

Additional functionality can be obtained by coupling of oxides to semiconductors. This concept will be presented with examples for the investigation of electronic transport across the oxide-semiconductor interface and its prospects for photoelectrocatalysis. Another example is the coupling between a monolayer of a non-ferroelectric oxide and silicon, which leads to interface-induced ferroelectric functionality.

With these examples I hope to provide a glimpse into the prospects and promise of combining functional oxides with semiconductors, and address some of challenges lying ahead.

N/A

In this talk I will present a new **experimental **technique capable of measuring the shape of the electrons in (super)conducting materials.

One-dimensional helical edge of a two-dimensional topological insulator is believed to be an ideal conductor, i.e. to be characterized by the universal conductance. This means that in contrast with ordinary one-dimensional particles, which are known to be always localized by arbitrary weak disorder, the states of chiral electrons are extended regardless of disorder. I will discuss the effect of localized spins - Kondo impurities. Provided that the electron-spin couplings is anisotropic this system can be mapped to the problem of the pinning of the ordinary charge density wave by a disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities eliminates effects of the topology and leads to the Anderson localization of the edge states. I will analyze existing experimental results in view of this conclusion.

We study an effective model of two interacting species of bosons in two dimensions, which is amenable to sign problem free Monte Carlo simulations. In addition to conventional ground states, we access a paired superfluid which is also a topological phase, protected by the remaining unbroken symmetry. This phase arises from the condensation of a composite object, the bound state of vortices and anti-vortices of one species, to a boson of the second species. We introduce a bulk response function, the Ising analog of the quantized Hall effect, to diagnose the topological phase. The interplay of broken symmetry and topology leads to interesting effects such as fractionally charged vortices in the paired superfluid. Possible extensions towards realistic models of cold atomic bosons will be discussed

We present a novel technique to image superparamagnetic iron oxide nanoparticles via their fluctuating magnetic fields. The detection is based on the nitrogen-vacancy (NV) color center in diamond, which allows optically detected magnetic resonance (ODMR) measurements on its electron spin structure. In combination with an atomic-force-microscope, this atomic-sized color center maps ambient magnetic fields in a wide frequency range from DC up to several GHz [1], while retaining a high spatial resolution in the sub-nanometer range

[2]. We demonstrate imaging of single 10 nm sized magnetite nanoparticles using this spin noise detection technique. By fitting simulations (Ornstein-Uhlenbeck process) to the data, we are able to infer additional information on such a particle and its dynamics, like the attempt frequency and the anisotropy constant [3]. This is of high interest to the proposed application of magnetite nanoparticles as an alternative MRI contrast agent or to the field of particle-aided tumor hyperthermia.

[1] E. Schäfer-Nolte et al., Phys. Rev. Lett. 113, 217204 (2014)

[2] P. Maletinsky et al., Nat. Nanotech. 7, 320 (2012)

[3] D. Schmid-Lorch et al., Nano Lett. 15, 4942 (2015)

Liquid helium 4 undergoes a phase transition into a superfluid at low temperatures. Owing to its quantum nature, the solid phase of helium 4 has been suggested to host a similar type of Bose-condensed state, supporting frictionless mass flow. This unique phenomenon has been termed supersolidity. In the past decade, the existence of supersolidity has been alternately confirmed and disproved experimentally. The controversy originates from the fact that a small supersolid signal can be overshadowed by large elastic effects arising from an anomaly in the shear modulus of the solid. Using a novel experimental approach, with specially-designed multi-mode torsional oscillators, we were able to accurately distinguish between the different contributions for the first time, and discovered a small frequency-independent signal, as expected in the presence of a supersolid phase. I will discuss the significance of our results in the broader context of the field's current state.

Research in graphene has evolved into a stage in which other isolated atomic planes of materials can now be reassembled in a chosen sequence, as in building with Lego where the blocks are defined with one-atomic-plane precision [1]. Due to their weak interlayer forces “Van der Waals” crystals can be separated to individual layers of a single crystallographic domain before reorienting and transferring them to form a new stack. The first part of the talk is aimed to give a wide review of the recent research done in Manchester in this field, with emphasize on ways to study materials which are unstable in ambient conditions [2].

The second part will focus on hetrostructures in which graphene is stacked between hexagonal boron nitride crystals (hBN), where electrons can travel for many micrometres before experiencing any scattering or de-coherence; I will first describe the extremely high superconducting currents which can be driven along graphene by placing it in proximity to a superconductor [3]. Remarkably, these currents persist even in the presence of high magnetic fields such that graphene can, in principle, be tuned into the Quantum Hall regime. The proximity-induced supercurrent, however, is found to be mediated by mesoscopic trajectories at the edges and its cut-off is prior to the onset of the QH. Next, I will discuss the nature of current flow when breaking the inversion symmetry of the system and opening an energy gap. Topological valley currents are predicted when placing the chemical potential in the gap. Lastly, I will present experimental observations of hydrodynamic-like flow and formation of electron-whirlpools in this system at higher temperatures [4].

[1] "Van der Waals heterostructures." Nature499.7459 (2013): 419-425.

[2] “Quality heterostructures from two dimensional crystals unstable in air by their assembly in inert atmosphere” Nano letters 15(8),4914 (2015).

[3] "Proximity superconductivity in ballistic graphene, from Fabry-Perot oscillations to random Andreev states in magnetic field." arXiv:1504.03286.

[4] "Negative local resistance due to viscous electron backflow in graphene." arXiv:1509.04165.

I will describe nonequilibrium dynamics in interacting quantum systems

mainly using the protocol of quenching the systems and following their evolution in

time. I'll discuss the evolution Lieb-Liniger system, a gas of interacting bosons

moving on the continuous infinite line and interacting via a short range potential.

Considering first a finite number of bosons on the line we find that for any value of

repulsive coupling the system asymptotes towards a strongly repulsive gas for any

initial state, while for an attractive coupling, the system forms a maximal bound

state that dominates at longer times. In either case the system equilibrates but does

not thermalize, an effect that is consistent with prethermalization. Then

considering the system in the thermodynamic limit - with the number of bosons and

the system size sent to infinity at a constant density and the long time limit taken

subsequently- I'll discuss the equilibration of the density and density-density

correlation functions for strong but finite positive coupling and show they are

described by GGE (generalized Gibbs ensemble) for translationally invariant initial

states with short range correlations. If the initial state is strongly non translational

invariant the system does not equilibrate. I will give some examples of quenches:

from a Mott insulator initial state or from a domain wall configuration or a Newton’s

Cradle. I also will show that if the coupling constant is negative the GGE fails for

most initial states in the Lieb-Liniger model. If time permits I shall discuss also the

quench dynamics of the XXZ Heisenberg chain.

Metal nanostructures are very attractive systems for confining and guiding light at the nanoscale. Being able to control their plasmon resonance could pave the way for realizing optical detectors and devices with both great spatial and spectral sensitivity. In this talk I will demonstrate local control of plasmons using two different nano-devices.

The first device consists of a single CdSe/ZnS quantum dot which is placed at a distance of a few nanometers from the surface of a gold nanoparticle. We control the distance between these two objects with a sub-nanometer precision using a technique where a short DNA strand is used as a spacer. By measuring the change in the exciton properties we were able to locally probe the plasmon resonance. We show that exciton absorption becomes sensitive to the excitation polarization and that the absorption and emission rates of the quantum dot can be enhanced by up to two orders of magnitude by the presence of the gold nanoparticle.

The second device consists of a single gold nanoparticle biased by two nanoscale electrodes. In this device, we control the emitted light spectrum by applying a bias voltage. Applying a large voltage induces inelastic electron tunneling in the device and generates plasmons which are detected by their radiative decay. We study the voltage dependence of the emitted spectrum and show a quantitative agreement with theory.

"Exciton–Plasmon Interactions in Quantum Dot–Gold Nanoparticle Structures" Eyal Cohen-Hoshen, Garnett W. Bryant, Iddo Pinkas, Joseph Sperling, and Israel Bar-Joseph Nano Letters 2012 12 (8), 4260-4264

"Fano Resonance in an Electrically Driven Plasmonic Device" Yuval Vardi, Eyal Cohen-Hoshen, Guy Shalem, and Israel Bar-Joseph, Nano Letters 2015 Submitted.

The presence of disorder in a non-interacting system can

localize all the energy eigenstates, a phenomena dubbed Anderson

localization. Many-body localization is an extension of this phenomena

to include interactions. Effects of interactions show up in the

logarithmic growth of entanglement after a global quench. We perform a

systematic study of the evolution and saturation of entanglement and

show that it can be used to detect the localization transition. We

consider the bipartite fluctuation which also captures the transition

and is promising as an experimental probe. We compare these results to

that of a non-interacting system and note important differences

between the two.

Interactions in Bose gas are usually modeled by a delta function potential

(i.e., each pair of particles interacts only where the positions of the two

particles coincide). This description ignores the range of interaction. We

calculated the effects of the finite range of the interactions. Inspired by

Van-der Waals potential, we proposed a one dimensional interaction potential of 3

delta functions, the central one is repulsive and the two peripheral ones

are attractive. This model introduces a length scale for the interaction

without giving up the mathematical simplicity of using delta functions. By

generalizing the work of Lieb and Liniger, we found an approximate Bethe-ansatz

solution for the spectrum of N interacting Bosons moving on a ring and showed

that the effect of interaction range might be crucial in some cases.

Joint work with Shmuel Fishman and Wolfgang Ketterle.

Charge density waves (CDWs) and superconductivity are canonical examples of

symmetry breaking in materials. Both are characterized by a complex order parameter –

namely an amplitude and a phase. In the limit of weak coupling and in the absence of

disorder, the formation of pairs (electron-electron for superconductivity, electron-hole for

CDWs) and the establishment of macroscopic phase coherence both occur at the

transition temperature Tc that marks the onset of long-range order. But, the situation may

be drastically different at strong coupling or in the presence of disorder. We have

performed extensive experimental investigations on pristine and intercalated samples of

2H-NbSe2, a transition metal dichalcogenide CDW material with strong electron-phonon

coupling, using a combination of structural (X-ray), spectroscopic (photoemission and

tunnelling) and transport probes. We find that Tc(δ) is suppressed as a function of the

intercalation-concentration δ and eventually vanishes at a critical value of δ=δc leading to

quantum phase transition (QPT). Our integrated approach provides clear signatures that

the phase of the order parameter becomes incoherent at the quantum/ thermal phase

transition, although the amplitude remains finite over an extensive region above Tc or

beyond δc. This leads to the persistence of a gap in the electronic spectra in the absence of

long-range order, a phenomenon strikingly similar to the so-called pseudogap in

completely different systems such as high temperature superconductors, disordered

superconducting thin films and cold atoms

Semiconducting nanowires have captured vast scientific attention ever since the first detection of a zero-bias conductance peak – possibly signifying a Majorana mode. It is therefore surprising how little information we gained in the time that have passed since that report. A major experimental obstacle is the brittleness and reactivity of the nanowires, that oxidize once brought into ambient conditions. By tackling this technological challenge we have been able to study spectroscopically the one-dimensional electronic states in bare InAs semiconducting nanowires. We visualize the one dimensional channels through the scattering of the electrons from point impurities on the surface of the nanowire. A series of stacking faults in the crystallographic structure form a Fabry-Perot interferometer that quantizes these states into resonances and allows us to extract the relaxation rate of these electrons as well as the strength of stacking fault as scatterers. Finally, at the end of the nanowire, where the Majorana modes should reside in the topological superconducting case, we find plethora of electronic states. These include quantized quantum-dot states at the tip of the nanowire that leak into the nanowire with strong electron-hole asymmetry, and a one-dimensional state that decays into the nanowire revealing an uncharted nonmonotonic regime in the decoherence of electrons in one dimension.

The design and synthesis of molecules that operate like microscopic machines is of fundamental importance. Such systems can be modelled theoretically by stochastic dynamics in which the system makes thermally activated transitions between a finite set of coarse-grained states. Artificial molecular machines can be driven away from thermal equilibrium in ways not found in biological molecular motors, in particular by time variation of external parameters. Such systems are often termed stochastic pumps. We demonstrate that a seemingly natural protocol of driving such systems does not work. We argue that this result holds also for systems of several particles with zero range interactions.

Recent experimental techniques have allowed to realize, in the so-called cold atomic systems, the quantum-coherent dynamics of many particles undergoing an arbitrary perturbation. Among the many application, one which has attracted a lot of interest is the possibility to study the evolutionof a non-equilibrium state of the Hamiltonian: the so-called quantum-quench protocols. When the spectrum of the Hamiltonian obeys some quite general conditions, local observables relax to a steady state described by the so-called “diagonal ensemble density matrix”, strictly depending on the eigenstates of the Hamiltonian. A question dating back to the origins of quantum mechanics is when the steady state is a thermal equilibrium one. It results, indeed, that this happens when the eigenstates are random states obeying the so-called Eigenstate Thermalization condition, but there is no general theory telling us precisely when this happens. This is quite different from classical thermalization induced by ergodic microscopic dynamics.

After having reviewed these results, clarifying the meaning of the words “integrable” and “ergodic”, I will discuss my recent work aimed to generalize them to the case of periodically driven systems. Noteworthy, even in this case, under conditions very similar to those of the quantum

quench, local observables relax to a steady condition described by the so-called “Floquet-diagonal density matrix”, very similar to its quenched counterpart. Here the observables in the steady condition are time-periodic and the energy-eigenstates are replaced by the Floquet states, which are the eigenstates of the stroboscopic dynamics. I will show numerical results on the Quantum Ising chain, which never thermalizes being integrable, and on its fully-connected counterpart, the Lipkin model. This quantum system has a well defined classical limit and it thermalizes to T = ∞ whenever the classical dynamics is ergodic. This thermalization is induced by the Floquet states obeying ETH and being extended in the Hilbert space. I will conclude the seminar moving from the discussion of local observables, with a well-defined classical limit, to truly quantum non-local objects like the fidelity.

References

[1] A. Russomanno, A. Silva, and G. E. Santoro, Phys. Rev. Lett 109, 257201 (2012), arxiv:1204.5084.

[2] A. Russomanno, A. Silva, and G. E. Santoro, J. Stat. Mech. p. P09012 (2013), arxiv:1306.2805.

[3] S. Sharma, A. Russomanno, G. E. Santoro, and A. Dutta, EPL 106, 67003 (2014).

[4] A. Russomanno, R. Fazio, and G. E. Santoro, arXiv (2014), arxiv:1412.0202

Sensitive and rapid detection of fluorescent dyes at low concentrations is a well-known challenge in many biological applications. Fluorescently labeled biosensors are widely used in specific DNA sequences detection and protein-protein interactions. Conventional genomic DNA (or RNA) detection methods predominantly rely on polymerase chain reaction (PCR) to achieve high sensitivity. However, PCR is costly, time consuming, and requires expertise in molecular biology. Hence, it is difficult for use in real time measurements. An early diagnosis lab tool should be compact, easy to operate, sensitive, and provide high throughput.

Here I present a novel technology termed Magnetic Modulation Biosensing (MMB) for rapid and highly sensitive detection of biomarkers. MMB relies on coupling magnetic beads to fluorescent labeled probes. Using two external magnetic poles, which are positioned on opposite sides of a small glass cell, the magnetic beads are aggregated into the detection area and set in a 1-D periodic motion, in and out of an orthogonal laser beam. The resulting periodic fluorescent light is collected by a photomultiplier and demodulated using a lock-in amplifier. The method offers high sensitivity since the magnetic field attracts the fluorescently labeled probes from the entire solution volume into a small detection area. The modulation and the narrow detection bandwidth separate the signal from the background noise of the non-magnetized solution. Moreover, the aggregation and modulation of the magnetic beads eliminate the need for separation and washing steps usually incorporated in heterogeneous assays, thereby shortening and facilitating the detection assay.

The MMB system is a generic device that has many applications. In general, any approach that produces fluorescent light as a result of the biorecognition event can utilize the MMB system to detect low concentrations of labeled probes. The ability to detect, for example, specific DNA sequences, rapidly, simply, and at low concentrations, is important for the development of a portable, high-throughput tool that enables early detection of pathogens and biomarkers.

We introduce notions concerning locally preferred structures and discuss

recent experimental and numerical results on metallic fluids that suggest

the onset of cooperative dynamics as a liquid is supercooled to form a

glass.

We will further suggest that certain quantum effects may emerge in the

high temperature limit of general "classical fluids". Towards this end, we

will invoke the WKB approximation, extend standard kinetic theory by

taking into account a possible minimal quantum time scale, apply ideas

from transition state theory, and relate (via Planck's constant) the

thermodynamic entropy to periods of semi-classical trajectories. Taken

together, these will suggest that, on average, the extrapolated high

temperature viscosity of general liquids may tend to a value set by the

product of the particle number density n and Planck's constant h.

Experimental measurements of an ensemble of 23 metallic fluids indicate

that might indeed be the case; the extrapolated high temperature viscosity

of each of these liquids divided (for each respective fluid) by its value

of nh veers towards a Gaussian with an ensemble average value that is

close to unity up to an error of size 0.6%. We invoke similar ideas to

discuss other transport properties to suggest how simple behaviors may

appear including resistivity saturation and linear T resistivity may

appear naturally. This approach suggests that minimal time lags may be

present in general fluid dynamics.

I review Raman data on iron pnictide and chalcogenides high-Tc superconductors.Below Tc one or two sharp well defined in-gap modes are observed for cross polarized Raman geometry. Next, I constrain the possible pairing symmetry relying on this data as well as ARPES, and neutron scattering.The in-gap modes are interpreted as Bardasis-Schrieffer and particle-hole excitons respectively consistent with the generalized s-wave pairing. Next I'll talk about the normal state data on parent compounds, AFe2As2, with A=Sr,Eu. The theory that yields a quasi-elastic scattering in terms of spin/orbital nematic correlations is presented.

Periodically driven quantum systems, such as semiconductors subject to light and cold atoms in optical lattices, provide a novel and versatile platform for realizing topological phenomena. Some of these are analogs of topological insulators and superconductors, attainable also in static systems; others are unique to the periodically driven case. I will describe how periodic driving, disorder, and interactions can conspire to give rise to new robust steady states, with no analogues in static systems. In disordered two-dimensional driven systems, a phase with chiral edge states and fully localized bulk states is possible; this phase can realize a non-adiabatic quantized charge pump. In interacting one dimensional driven systems, current carrying states with excessively long life times can arise.

In recent years we have been involved in the search for Majorana fermions (MF) in topological superconducting thin films [1-3]. The idea was to induce superconductivity in the doped topological insulator Bi_{2}Se_{3 }by the proximity effect when it is sandwiched in a bilayer with an s-wave superconductor. For this we deposited bilayer thin films of Bi_{2}Se_{3}-NbN from which we prepared junctions of Bi_{2}Se_{3}-NbN-Au. Conductance spectra results of these junctions showed robust zero bias conductance peaks, which indicate unconventional superconductivity, but did not provide a conclusive evidence for MF. In the past year we investigated ultra-thin bilayers of Bi_{2}Se_{3}-NbN, and compared their properties to those of bare NbN reference films of the same thickness [4]. In my talk I shall discuss some of our recent results, in particular, gating effects of these bilayers, where significant magnetoresistance structures are observed also above the superconducting transition temperature.

[1] G. Koren, T. Kirzhner, E. Lahoud, K. B. Chashka, and A. Kanigel, Phys. Rev. B 84, 224521 (2011).

[2] G. Koren and T. Kirzhner, Phys. Rev. B 86, 144508 (2012).

[3] Gad Koren, Tal Kirzhner, YoavKalcheim and Oded Millo, EPL 103, 67010, (2013).

[4] Gad Koren, Supercond. Sci. Technol. 28, 025003 (2015).

The Fermi surface - a discontinuity in the momentum distribution - is a hallmark of fermionic ensembles. Its existence even for interacting systems forms the basis for Landau’s celebrated Fermi liquid theory. Understanding under what circumstances the Fermi surface collapses and Fermi liquid theory breaks down is one of the long-standing challenges in condensed matter physics. We study this question experimentally with a strongly interacting ultracold Fermi gas in the BCS-BEC crossover regime. The nature of the normal state of the gas in the BCS-BEC crossover is an intriguing and controversial topic, both experimentally and theoretically. While the many-body ground state is always a superfluid condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules as a function of the interaction strength. We measure the distribution of single-particle energies and momenta (spectral function) in a homogeneous gas above Tc. Fits to data taken for different interaction strengths reveal the onset of pairing and decreasing spectral weight (or quasiparticle residue, Z) for the Fermi liquid. We extract the effective mass m, pair correlation length, and Tan’s contact. Surprisingly, we find that Z vanishes abruptly and not gradually with increasing interaction, which signals a sudden breakdown of a Fermi liquid description and the disappearance of the Fermi surface.

Spintronics is expected to play an important role towards the quest for more power efficient electronics, by utilizing besides the charge degree of freedom also the electron spin. Key physical phenomena to enable efficient charge-to-spin current conversion, and vice versa, are spin Hall effects, which generate transverse spin current from charge currents even in non-magnetic conductors. In order to gain insight into the underlying physical mechanism and to identify technologically relevant materials, it is important to quantify the spin Hall angle g, which is a direct measure of the charge-to-spin conversion efficiency [1]. We developed a measurement approach based on spin pumping, which enables us to quantify even small spin Hall angles with high accuracy [2,3]. Spin pumping utilizes microwave excitation of a ferromagnetic layer adjacent to a normal metal to generate a homogeneous *dc* spin current over a macroscopic area. Thickness dependent measurements also allow the determination of spin diffusion lengths, which are essential for a proper quantification of spin Hall effects [4,5]. This approach can be used to detect spin Hall effects in a wide variety of materials, including metallic antiferromagnets [6]. Furthermore, we have shown how magnetic proximity effects can reduce spin Hall conductivities in one of the most widely used material for spin current detection: Pt.

In the second part of my presentation, I will discuss how spin Hall effects can be used for the manipulation of spin textures. In magnetic films with perpendicular anisotropies, magnetostatic interactions can stabilize magnetic skyrmion bubbles. By adding an additional layer with strong spin-orbit coupling to the ferromagnet, it is possible to generate an interfacial chiral Dzyaloshinskii Moriya interaction, which stabilizes the skyrmion spin structure in the magnetic bubble domain wall. Using spin Hall effects these magnetic skyrmion bubbles can then be electrically manipulated. This is demonstrated for completely metallic systems, where we can generate skyrmions through inhomogeneities of electric charge currents in a process that is remarkable similar to the droplet formation in surface-tension driven fluid flows. This provides a practical approach for skyrmion formation on demand.

refs in pdf

The recent discovery of signatures consistent with Majorana fermions in topological superconductors may open the door to their future use in qubit devices. In this talk I will describe theoretical advances in the field of hybrid superconducting circuits that combine semiconductors and superconductors to form new types of topologically protected qubits. Given the time I will also survey experimental progress in these directions.

The state formed at the interface between two materials often offers unique and exciting properties. For instance, modern electronics is heavily based on such interfaces. A decade ago, a new conducting interface was discovered between the two insulating materials LaAlO_{3} and SrTiO_{3}. The interface was soon found to host many interesting properties including superconductivity, magnetism, resistive switching and the possibility to easily create nanowires at the interface. This spurred a lot of interest in the system, but despite the extensive research, fundamental questions remains such as what the origin of the emergent properties is, and how appealing interface properties can be found and tailored.

Here, we show that replacing LaAlO_{3} with different complex oxide films opens up new avenues to answer these questions. By the right choice of substitutes for LaAlO_{3}, one can end up with heterostructures where the origin of the interface conductivity is unambiguous and simple. In addition, more perfect heterostructures can be synthesized, giving rise to e.g. enhanced electron mobility and the emergence of quantum magnetotransport properties at low temperatures.

We have studied the electronic transport in GaAs and InAs one dimensional quantum wires. We have observed that in disordered wires the electronic transport is strongly affected by the Coulomb interactions. The experimental results are well described in the framework of so called Luttinger liquid theory. We find the value of the Luttinger interacting parameter for our wires. The conductance peaks observed in Coulomb blockade regime in InAs wires reduce their values at low temperature in contrast with the Coulomb blockade peaks reported so far in all the experiments in other material systems. This phenomenon was predicted theoretically [1] for the materials with the Luttinger Interaction parameter g<1/2.

In the presentation, I will give few possible explanations why the effective Luttinger parameter g in the InAs wires is smaller than the one observed in other 1D systems, like Carbon nanotubes, or GaAs quantum wires reported so far.

[1] A. Furusaki, Phys. Rev. B 57, 7141 (1998).

The study of electrical properties of semiconducting nanocrystals (NCs) poses fundamental as practical difficulties. While control of the optical characteristics of these objects by size and shape is well understood, precise modification of the electronic properties, beyond the band-gap, is still challenging. We have taken a combined macroscopic-nanoscopic approach to investigate the electronic properties of Cu2S NCs. First, a semiconductor-metallic hybrid structure, comprising a Cu2S NC encapsulated by a Ruthenium cage-like shell. The growth of a metallic component induces semiconductor metallic synergistic behavior and unique negative differential conductance features in the tunneling spectra. Second, we discovered a new impurity free mechanism for NC doping, by thermal treatment at moderate temperatures, thus creating vacancies leading to free charge carriers. This thermal doping method is applied to Cu2S-NC arrays, where Cu vacancies easily form, resulting in p-type doping and achieving up to 6 orders of magnitude conductance enhancement. We succeeded also in demonstrating local thermal doping via a focused laser beam serving as the heating source, opening an innovative route for low-temperature patterned doping of NC arrays.

- “Thermal doping by vacancy formation in copper sulfide nanocrystal arrays”, K.Vinokurov, S.Keren-Zur, I. Hadar, Y. Schilt, U. Raviv, O.Millo, U.Banin, NanoLetters,2014, DOI:10.1021/nl4043642
- “Periodic negative differential conductance in a single metallic nanocage”

Y.Bekenstein, K.Vinokurov, TJ.Levy, E.Rabani, U.Banin, O.Millo

Physical Review B 86 (8), 085431(2012) - “Electronic properties of hybrid Cu2S/Ru semiconductor/metallic-cage nanoparticles”

Y.Bekenstein, K.Vinokurov, U.Banin, O.Millo

Nanotechnology 23 (50), 505710(2012) - “Charge transport in Cu2S nanocrystal arrays a study of crystal size and ligand length”, O.Elimelech, K.Vinokurov, O.Millo, U.Banin Zeitschrift für Physikalische Chemie (2014)

In disordered systems, the electronic ground state is the result of a competition between Coulomb interactions, disorder, which eventually leads to localization of charge carriers, and, when relevant, superconductivity. In this conflict between antagonistic forces, dimensionality plays a special role and determines what ground states are allowed. Indeed, in three-dimensional systems, two distinct quantum phase transitions, the metal-to-insulator transition (MIT) and the superconductor-to-metal transition, separate the three possible ground states. By contrast, in two dimensions, the system can only exhibit a direct superconductor-to-insulator transition (SIT), since metals are theoretically forbidden in the absence of strong electron-electron interactions. One important question is then to understand how the three ground states (superconducting, metallic, and insulating) that are possible in bulk systems evolve when the thickness is reduced.

Thin alloy films provide interesting systems to address this question. I will report on the disorder-induced quantum phase transitions in amorphous Nb_{x}Si_{1-x} thin films. The disorder is here tuned by three different parameters: the Nb composition, the thickness and the annealing temperature. Low temperature DC measurements reveal unexpected dissipative states after the destruction of the superconducting long range order. These states then evolve towards an insulating state. Our results provide an insight on the entanglement between the MIT and the SIT.

Flying insects can perform a wide array of extreme aerial maneuvers with exquisite accuracy and robustness, outmaneuvering any man-made flying device. As a physical system, a flapping insect is strongly nonlinear with fast-growing mechanical instabilities that must be controlled to allow flight. Hence, similar to balancing a stick on one's fingertip, flapping flight is a delicate balancing act made possible only by ever-present, fast corrective actions. Understanding the underlying mechanisms of insect flight is a major challenge, since this graceful behavior is highly coupled to complex fluid flows and arises from the concerted operation of physiological functions across multiple length and time scales. As such, Insect flight research involves basic concepts from nonlinear dynamics, fluid mechanics, neurobiology and control theory, and has direct application to the development of small flapping robots.

Here we show how flies control their rotational degrees of freedom: yaw, pitch and roll. We focus on their body roll angle, which is unstable and most sensitive degree of freedom. We glue a magnet to each fly and apply a short magnetic pulse that rolls it in mid-air. Fast video shows that flies fully correct for perturbations of up to 100^{o} within 30-+7 ms. The roll correction maneuver consists of a stroke-amplitude asymmetry that is well described by a linear PI controller. For more aggressive perturbations, we show evidence for nonlinear and hierarchical control mechanisms. Flies respond to roll perturbations within a single wing-beat, or 5 ms, making this correction reflex one of the fastest in the animal kingdom.

We have investigated electron transport in a quasi-one dimensional electron gas where the confinement potential can be progressively weakened so resulting in the energy levels decreasing in energy relative to each other. However the decline occurs at different rates which is attributed to the electron-electron repulsion varying with the shape of the wavefunction. When the former ground state crosses the higher levels we find missing plateaux of quantised conductance, this can also be observed in the increase in the capacitance between the confining gates and the electron gas. Studies of the movement of the levels shows that both crossings and anti-crossings can be observed, this will be discussed along with other consequences of the way the levels interact. The role of the interactions in giving rise to the spin dependent 0.7 structure will be presented.

Many-body localization is a peculiar dynamical transition between ergodic and non-ergodic phases, which may occur at any temperature and in any dimension. Current theory suggest that for temperatures below the transition the system is non-ergodic and localized, such that conductivity vanishes at the thermodynamic limit, while for temperatures above the transition the system is thermal and conductive. In this talk I will present a study of ergodicity and dynamical properties of the many-body localization transition using a combination of non-equilibrium diagrammatic techniques and numerically exact methods. I will present the dynamical phase-diagram at infinite temperature, and provide evidence of existence of a novel phase, which is ergodic yet has a vanishing DC conductivity.

Over recent years, a growing interest in the properties of molecular junction, typically described by coupling of individual molecules (quantum dots) to macroscopic electrodes under nonequilibrium conditions, has raised fundamental and conceptual issues regarding the physics of nanometer scale systems, as well as those of the low dimensional mesoscopic systems in which they share certain qualities. Theory faces several important challenges: first, the existence of more than one steady-state in these type of systems has been a matter of debate, both in the context of simple impurity models and in the case of inelastic tunneling channels. Second, characterization of the relevant time scales under the role of molecular vibrations, environmental disorder and dissipation is not yet fully understood. In order to address these issues, I will present an exact theory which enable us to study both dynamical and steady state properties. The theory, based on the Nakajima-Zwanzig equations, relies on the fact that out of equilibrium system posses a so called memory terms. Apparently, this memory term, also known in the literature as a non-Markovian effect, holds a significant amount of information regarding transient properties as well as those of the system's relaxation. This would facilitate our understanding of elastic and inelastic transport phenomena, where the nature of both coherent and incoherent transport is crucial for a complete picture.

NanoSQUIDs residing on the apex of a quartz tip (SOT), suitable for scanning probe microscopy with record size, spin sensitivity, and operating magnetic fields, are presented[1]. We have developed SOT made of Pb with an effective diameter of 46 nm and flux noise of Φn = 50 nΦ0/Hz1/2 at 4.2 K that is operational up to unprecedented high fields of 1 T[2]. The corresponding spin sensitivity of the device is Sn = 0.38 μB/Hz1/2, which is about two orders of magnitude more sensitive than any other SQUID to date. A limitation which is common to all scanning SQUID systems is their sensitivity to only one component of the magnetic field. Recently, a new device that is fabricated by pulling a quartz tube with a “θ” shaped cross section overcomes this limitation [3]. This geometry gives rise to two parallel SQUID loops sharing a common branch. Using a focused ion beam, we then etch the tip so that the two SQUID loops become oblique with respect to each other. As a result of the 3D structure, the SQUID can be tuned in-situ to be sensitive to two orthogonal components of the magnetic field.

We use this technique to study vortex matter in superconductors. At low vortex density and low currents, we measure the fundamental dependence of the elementary pinning force of multiple defects on the vortex displacement. The outstanding magnetic sensitivity of the SOT allows probing vortex displacements as small as 10 pm. This study reveals rich internal structure of the pinning potential and unexpected phenomena such as softening of the restoring force and abrupt depinning. The results shed new light on the importance of multi-scale random disorder on vortex dynamics and thermal relaxation. At high vortex density and high currents, we image the flow patterns of moving lattice revealing dynamic instabilities, plastic flow, and ordering.

[1] A. Finkler, Y. Segev, Y. Myasoedov, M. L. Rappaport, L. Neeman, D. Vasyukov, E. Zeldov, M. E. Huber, J. Martin and A. Yacoby, Nano Lett. 10, 1046 (2010)

[2] D. Vasyukov, Y. Anahory, L. Embon, D. Halbertal, J. Cuppens, L. Neeman, A. Finkler, Y. Segev, Y. Myasoedov, M. L. Rappaport, M. E. Huber, and E. Zeldov, Nature Nanotech. 8, 639 (2013).

[3] Y. Anahory, J. Reiner, L. Embon, D. Halbertal, A. Yakovenko, Y. Myasoedov, M.L. Rappaport, M. Huber and E. Zeldov, Nano Lett. (in press)

The study of interacting many-body physics is traditionally focused on condensed matter, where electrons interact via Coulomb repulsion and create a rich panoply of correlated states. Observing these delicate quantum states demands pristine environments and locally-defined potentials. The challenges of realizing and probing materials systems, however, has driven the creation of quantum simulators, which are clean and tunable by design, but are typically composed of bosonic constituents with weak interactions. Can we make a condensed matter system with the cleanliness and tunability of a quantum simulator? In this talk, I will describe how a new technique allows us to use carbon nanotubes to create pristine 1D electron systems with unparalleled tunability, and how these devices serve as ideal scanning probes to image the spatial correlations of delicate 1D quantum states. These capabilities open the possibility for a new generation of condensed matter experiments exploring interacting electrons, spins, and nano-mechanics in precision-designed potential landscapes.

In this talk I will discuss the phenomena of dephasing and phase lapses as they occur in two setups operating in the quantum Hall regime. Both setups consist of a quantum dot and an electronic Mach-Zehnder interferometer. Dephasing, i.e. loss of coherent transport, and phases lapses, i.e. abrupt jumps in the phase of the transmission amplitude, turn out to be intimately related in these setups.

In the first setup, transport through a chiral channel is affected by charge fluctuations in a nearby quantum dot [1]. We have studied this setup both in the integer and in the fractional quantum Hall regimes with filling factors 2 and 4/3, respectively [2]. It is found that the regime of operation strongly affects the amount of dephasing and the occurrence (or absence) of phase lapses. Evaluation of the *concurrence* in the system sheds light on the absence of full dephasing observed in the fractional regime. Recent experimental results will be also discussed [3].

In the second setup transport through a quantum dot operating in the quantum Hall regime with filling factor 2 is analyzed [4]. Similarly to the zero magnetic field case [5], phase lapses occur also here. However, the mechanism responsible for their occurrence is substantially different. It will be shown that certain degrees-of-freedom of the quantum dot act as a dephasor to the coherent transport through the quantum dot.

I will present recent results obtained both theoretically and

experimentally on fractal spectral properties of a polariton gas in a

Fibonacci quasi-periodic potential. The observed spectrum is

accurately reproduced from a theoretical model that we shall present.

We have observed for the first time log-periodic oscillations and the

opening of mini-gaps following the gap labeling theorem. These results

illustrate the potential of cavity polaritons as a quantum simulator

in complex topological geometries.

Graphene and topological insulators are both materials where electronic transport properties are dictated by relativistic energy-momentum dispersion relations. Several topological insulators, such as Bi_{2}Se_{3}, have a layered structure, with weak out-of-plane van-der-Waals bonds, allowing for easy exfoliation into thin flakes. In the talk I will describe how layered materials such as graphene and Bi_{2}Se_{3} can be vertically stacked, creating a new kind of heterostructure. In electronic devices fabricated from such heterostructures, each material is contacted individually, and electronic properties of the interface are measured at low tempertures. The measurements reveal that the interface is a tunnel junction of exceptionally good quality. This tunnel junction can then be used to perform mutual inelastic spectrocsopy, revealing the phonon spectra of both materials, and to measure the density-dependent spectra of graphene and bilayer graphene.

Since the initial discovery of skyrmion lattices in chiral magnets [1], there has been a tremendous growth in this field as an increasing number of compounds are found to have extended regions of stable skyrmion lattices [2] even close to room temperature [3]. These systems have significant promise for applications due to their size scale and the low currents or drives needed to move the skyrmions [4]. Another interesting aspect of skyrmions is that the equations of motion have significant non-dissipative terms or a Magnus effect which makes them unique in terms of collective driven dynamics as compared to other systems such as vortex lattices in type-II superconductors, sliding charge density waves, and frictional systems. We examine the driven dynamics of skyrmions interacting with random and periodic substrate potentials using both continuum based modelling and particle based simulations. In clean systems we examine the range in which skyrmion motion can be explored as a function of the magnetic field and current and show that there can be a current-induced creation or destruction of skyrmions. In systems with random pinning we find that there is a finite depinning threshold and that the Hall angle shows a strong dependence on the disorder strength. We also show that features in the transport curves correlate with different types of skyrmion flow regimes including a skyrmion glass depining/skyrmion plastic flow region as well as a transition to a dynamically reordered skyrmion crystal at higher drives. We find that increasing the Magnus term produces a low depinning threshold which is due to a combination of skyrmions forming complex orbits within the pinning sites and skyrmion-skyrmion scattering effects. If the skyrmions are moving over a periodic substrate, with increasing drive the Hall angle changes in quantized steps which correspond to periodic trajectories of the skyrmion that lock to symmetry directions of the substrate potential.

[1] S. Muhlbauer et al Science 323 915 (2009).

[2] X. Z. Yu et al. Nature 465, 901–904 (2010).

[3] X.Z. Yu et al Nature Materials, 10, 106 (2011).

[4] A. Fert, V. Cros, and J. Sampaio Nature Nanotechnology 8, 152 (2013).

What are random matrices? Why are they useful in physics? What is

their predictive power? These questions will be answered in the first

part of the talk, and the connection between random matrices and

chaotic systems shown.

Random matrices find applications in such diverse fields of physics as

disordered systems, many-body quantum systems, chiral symmetry

breaking in QCD, and even beyond physics in number theory. Some of

these will be discussed in the remainder of the talk.

We have measured the electronic-structure of FeSe$_x$Te$_{1-x}$ above and below T$_c$ using ARPES. In the normal state we find multiple bands with remarkably small values for the Fermi energy $\varepsilon_F$. Yet, below T$_c$ we find a superconducting gap $\Delta$ that is comparable in size to $\varepsilon_F$, leading to a ratio $\Delta/\varepsilon_F\approx 0.5$ that is much larger than found in any previously studied superconductor. We also observe an anomalous dispersion of the coherence peak which is very similar to the dispersion found in cold Fermi-gas experiments and which is consistent with the predictions of the BCS-BEC crossover theory.

During the last 20 years, the possibility of fabricating nanoscale samples has opened the possibility to study critical phenomena in reduced dimension systems. This includes strong thermal fluctuations, fluctuations of the order parameter, the weakening of the interactions involved and the onset of a competition between surface and volume effects; the major pending question being the existence of singularities of thermodynamic functions at the phase transition in 0D, 1D or 2D magnetic or superconducting systems. Thanks to innovative experimental development based on suspended sensors made at Institut Néel, a very sensitive thermal experiment permits the measurement of specific heat signatures of very small mass sample (down to the nanogram) [1].

In this presentation, I will detail recent experiments demonstrating the power of the specific heat tool to study phase transitions at low dimension. Various illustrations will be given starting from magnetic materials like CoO down to very small thickness (few nm) where a significant reduction in the Néel temperature of CoO ultra-thin films has been revealed. It is found that the films consist of weakly coupled antiferromagnetic (AF) grains. The T_{N} reduction from large to small grain samples scales with the grain size reduction, according to the Binder theory of critical phenomena in systems of reduced dimensions.

Then, I will present measurements performed on submicron mesoscopic superconductors (ring, disk) where phase transitions between different vortex states have been evidenced as a function of applied magnetic field [2,3]. Finally, I will review recent experimental development allowing the measurement of in situ cold deposited superconducting thin films close to the insulating regime. A quench condensed apparatus has been mounted permitting the deposition of the sample directly on the Si membrane sensors at low temperature. Heat capacity measurement can be done continuously as a function of the thickness in granular or ultra-thin film through the insulator to superconducting transition [4]. This innovative equipment paves the way to new measurement of specific heat anomaly in low dimensional systems, in the presence of fluctuations or close to a Quantum Phase Transition.

The disorder-driven superconductor to insulator transition (SIT) is considered to be a prototype of a quantum phase transition at zero temperature. Lately, there has been a renewed interest in this field due to the experimental observations of a number of dramatic features near the SIT of amorphous superconducting materials such as indium oxide and niobium nitride. These novel features included the simple activated temperature dependence of the resistance in the insulating side, a large peak in the magneto resistance, peculiar I-V characteristics and traces of superconductivity at temperatures above Tc. We present experimental results from tunneling spectroscopy, Terahertz spectroscopy and transport measurements that shed light on the physical mechanism governing this phase transition. Our key observations are: 1 - Superconducting gap in the insulating side of the transition. 2 - A possible experimental evidence for collective modes (namely the "Higgs" amplitude mode) in such disordered films close to the SIT. 3 - The possibility to tune the quantum phase transition simply by screening the e-e interactions. These results and their possible consequences will be discussed.

Careful transport measurements near the superconductor-insulator transition in amorphous indium-oxide reveal a symmetry relating states in the insulator to those in the superconducting phase. I will discuss this symmetry and its consequences, and show that it is violated upon entering the strong insulator at low temperatures.

Although solid He does not exhibit bulk supersolidity, there is evidence that grains of solid can move inside a solid matrix.

To observe a flow of solid directly, we constructed a "microphone" embedded in solid He contained inside a torsional oscillator.

The microphone can detect vibrations down a few percent of a lattice constant.

Our idea was that if the solid He flows past the microphone, the atomic corrugation of its surface should generate vibrations at a

frequency f = flow speed/lattice constant. We indeed found that solid He can flow while maintaining its solid structure.

At our lowest temperature of 0.5K, a frictionless flow of solid was observed, in agreement with the prediction that grain boundaries can be superfluid.

Why are the pyrochlore crystals R2Ti2O7 "quantum" magnets? Beginning with

this question,this talk will introduce concepts of quantum magnetism on

the pyrochlore lattice. The symmetry of the lattice and of quantum

mechanical spin states will be described. Using symmetry arguments, the

most general form of a spin=1/2 quantum exchange model for the pyrochlore

crystal can be written down. Symmetry considerations also yield a map

between rare earth spin states and spin=1/2 states, leading to a universal

model of "anisotropic exchange" for rare earth pyrochlores. This model

contains four coupling constants, which have been determined

experimentally for various rare earth pyrochlores.

I review the concept of thermalization of light in systems of coupled nonlinear optical waveguides within the framework of the tight-binding model with nonlinearity.

In many cases of interest the energy and power conservation laws enable the formulation of the equilibrium properties of such systems in terms of the Gibbs measure with positive temperature.

As a particular example I will consider the statistics of two nonlinearly coupled vector fields relevant to the propagation of polarized light in discrete waveguides in the presence of the four-wave mixing. In the limit of the

large nonlinearity an analytical expression for the distribution of Stokes parameters can be obtained which is found to be dependent only on the statistical properties of the initial polarization state and not on the strength of nonlinearity.

The interest in magnetization reversal in nanostructures mainly focuses on two phenomena: the superparamagnetic behavior at a temperature range below the Curie temperature and the expected crossover between thermally-activated reversal to reversal dominated by macroscopic quantum tunneling at sufficiently low temperatures. Here we explore both phenomena by monitoring individual reversals in nanostructures of SrRuO_{3} and obtain novel insight of both phenomena. In particular, we show for the first time the applicability of the Langevin equation to superparamagnetic fluctuations of an individual volume [1] and we find compelling indication for magnetization reversal dominated by macroscopic quantum tunneling below a record high temperature of 10 K [2].

**References**

- O. Sinwani, J. W. Reiner, and L. Klein (2014). Monitoring superparamagnetic Langevin behavior of individual SrRuO
_{3}nanostructures. Phys. Rev. B 89 020404(R). - O. Sinwani, J. W. Reiner, and L. Klein (2012). Indication for macroscopic quantum tunneling below 10 K in nanostructures of SrRuO
_{3}. Phys. Rev. B 86 100403(R).

Superconducting quantum interference devices (SQUIDs) are among the most sensitive

sensors for magnetic field, and nanoscale SQUIDs, in particular, also have high

sensitivity to magnetic dipole fields. The sensitivity of SQUIDs with submicron sensor

areas is better than ~100 µB/√Hz, where µB is the Bohr magneton, the magnetic dipole

moment of the electron. When coupled with a scanning platform, these nanoscale

SQUIDs become powerful tools for studying properties of magnetic systems, including

persistent currents in normal metal rings, local measurements of penetration depths in

high Tc

superconductors, vortex dynamics in type II superconductors, and imaging edge

currents in topological insulators. I will describe two such nanoscale SQUID sensors,

planar SQUID susceptometers with sensitivities of ~70 µB/√Hz and needle-like SQUID

magnetometers with sensitivities better than 1 µB/√Hz, concluding with recent results of,

and future plans for, studies using these sensors.

We present an analytical study of diamagnetism and transport in a film with superconducting phase fluctuations, formulated in terms of vortex dynamics within the Debye-Hückle approximation. We find that the diamagnetic and Nernst signals decay strongly with temperature in a manner which is dictated by the vortex core energy. Furthermore, we find that at high temperatures the ratio between the magnetization and the transverse thermoelectric conductivity tends to a constant, determined by the variation of the core energy near the edges of the system. We use the theory to interpret measurements of underdoped La2-xSrxCuO4 above the critical temperature regime and obtain a considerably better fit to the data than a fit based on Gaussian order-parameter fluctuations. Our results indicate that the core energy in this system scales roughly with the critical temperature. The onset of the Nernst effect lies in a regime which can not be described in terms of a liquid of well defined vortices and involves substantial amplitude fluctuations.

TBDWe construct a scattering matrix formulation for the topological classification of one-dimensional superconductors with effective time reversal symmetry in the presence of interactions. For a closed geometry, Fidkowski and Kitaev have shown that such systems have a $\mathbb{Z}_8$ topological classification. We show that in the weak coupling limit, these systems retain a unitary scattering matrix at zero

temperature, with a topological index given by the trace of the Andreev reflection matrix, $\mbox{tr}\, r_{\rm he}$. With interactions, $\mbox{tr}\, r_{\rm he}$ generically takes on the finite set of values $0$, $\pm 1$, $\pm 2$, $\pm 3$, and $\pm 4$. We show that the two topologically equivalent phases with $\mbox{tr}\, r_{\rm he} = \pm 4$ support emergent {\it many-body} end states, which we identify to be a topologically protected Kondo-like resonance. The path in phase space that connects these equivalent phases crosses a non-fermi liquid fixed point where a multiple channel Kondo effect develops. Our results connect the topological index to transport properties, thereby highlighting the experimental

signatures of interacting topological phases in one dimension.

The problem of dissipationless spin transport (spin superfluidity) has occupied the minds of condensed matter physicists for decades. The interest to this problem revived nowadays in connection with the emergence of spintronics. It was in the past, and still is, a matter of controversy. One source of controversy is that spin is not a conserved quantity. This leads to many complications and ambiguities in defining such concepts as spin current, or spin transport. Sometimes these complications are purely semantic, but they can be and were a serious obstacle for understanding physics and for deriving proper conclusions concerning observation and practical application of the phenomenon. The talk will address these problems, connection of spin superfluidity with magnon BEC among them.

A prominent example of anisotropic spin-orbital models is the Kitaev-Heisenberg (KH) model on

the honeycomb lattice [1,2]. This model was proposed as the minimal model to describe the low-

energy physics of the quasi two-dimensional compounds, Na2IrO3 and Li2IrO3. In these compounds,

Ir4+ ions are in a low spin 5d5 conguration and form weakly coupled hexagonal layers. Due to

strong SOC, the atomic ground state is a doublet where the spin and orbital angular momenta of Ir4+

ions are coupled into Je

= 1=2. The KH model describing the interactions between Je

moments

contains two competing nearest neighbor interactions: an isotropic antiferromagnetic Heisenberg

exchange interaction originated mainly from direct direct overlap of Ir t2g orbitals and a highly

anisotropic Kitaev exchange interaction [3] which originates from hopping between Ir t2g and O 2p

orbitals via the charge-transfer gap.

We study critical properties of the KH model on the honeycomb lattice at nite temperatures [4,5].

The model undergoes two phase transitions as a function of temperature. At low temperature,

thermal uctuations induce magnetic long-range order by order-by-disorder mechanism. This mag-

netically ordered state with a spontaneously broken Z6 symmetry persists up to a certain critical

temperature. We nd that there is an intermediate phase between the low-temperature, ordered

phase and the high-temperature, disordered phase. Finite-size scaling analysis suggests that the

intermediate phase is a critical Kosterlitz-Thouless phase with continuously variable exponents. We

argue that the intermediate phase has been likely observed above the magnetically ordered phase

in A2IrO3 compounds.

[1] G. Jackeli and G. Khaliullin, Phys. Rev. Lett. 102, 017205 (2009).

[2] J. Chaloupka, G. Jackeli, and G. Khaliullin, Phys. Rev. Lett. 105, 027204 (2010).

[3] A. Kitaev, Ann. Phys. 321, 2 (2006).

[4] C. Price and N. B. Perkins, Phys. Rev. Lett. 109, 187201 (2012).

[5] C. Price and N. B. Perkins, Phys. Rev. B 88, 024410 (2013).

I will present scanning tunneling spectroscopy measurements performed on half-metallic ferromagnetic La_{2/3}Ca_{1/3}MnO_{3} (LCMO) films of variable thicknesses epitaxially grown on two types of high temperature superconductor films: the hole-doped YBa_{2}Cu_{3}O_{7-}_{d} (YBCO) and the electron doped Pr_{1.85}Ce_{}CuO_{4} (PCCO). Surprisingly, our tunneling spectra reveal long-ranged penetration of superconductor order parameter into the LCMO layer, to distances as long as 30 nm, an order of magnitude larger than the expected coherence length associated with singlet-pairing superconductivity in LCMO. This anomalous proximity effect manifests itself in the tunneling spectra as gaps and zero-bias conductance peaks (ZBCPs), and in some cases split-ZBCPs. Our observations are accounted for by the emergence of parallel-spin triplet-pairing superconductivity at the bilayer’s interfaces, promoting the long-ranged proximity effect. The appearance of ZBCPs indicates that the orbital symmetry of the induced order parameter is anisotropic and sign-changing, of either *d*-wave of *p*-wave character, corresponding to an odd or even dependence on the Matsubara frequency, respectively, and possibly also of a complex symmetry, e.g., *p _{x}+ip_{y}*. The latter symmetry was also observed in our tunneling spectra measured on the topological insulator Bi

_{2}Se

_{3}deposited on the

*s*-wave superconductor NbN. Finally, I will discuss the effect of applied magnetic field on the proximity effect. Interestingly, a non-monotonic behavior was observed, where the proximity effect first increased and then suppressed with magnetic field. The consequence of this behavior regarding the possible mechanisms yielding induced triplet superconductivity, and the corresponding role of magnetic inhomogeneity, will be discussed.

A band with a nontrivial topology, as characterized by a nonzero Chern number, is called a Chern band. When such a band is filled, it displays a quantized integer Hall conductance. Recent numerics show that when such a band is partially full and the electrons in it are subject to strong repulsive interactions, ground states reminiscent of fractional quantum Hall states are found at particular fractional filling. I will show that this is not an accident by constructing an algebraically exact mapping from such bands to fractional quantum Hall problems in terms of operator-based Composite Fermions. On the lattice, one can realize not only the usual FQH states of the continuum, but also states whose existence depends on the lattice, and whose filling can be different from the Hall conductance.

In this talk I will describe the quench dynamics of isolated interacting systems in 1-d, governed by integrable Hamiltonians . I shall study the time evolution of a gas of interacting bosons moving on the continuous infinite line and interacting via a short range potential (the Lieb-Liniger model). For a system with a finite number of bosons we find that independently of the initial state the system asymptotes towards a strongly repulsive gas for any value of repulsive coupling, while for any value of attractive coupling, the system forms a maximal bound state that dominates at longer times. In either case the system equilibrates but does not thermalize, an effect that is consistent with prethermalization. For an infinite system we find that the system equilibrates to a generalized Gibbs ensemble. If time permits I shall discuss also the quench dynamics of the XXZ Heisenberg chain and of a mobile impurity in an interacting Bose gas (quantum Brownian motion).

The rise of graphene has marked the beginning of a renaissance for the almost forgotten class of layered materials. Layered materials are composed of two dimensional sheets of r strongly intralaye bonded compounds stacked together by weak interlayer VdW forces.

Similarly to graphene, the two-dimensional building block of graphite, quantum confined layers of such materials possess fascinating physical properties. Among such properties are the (pseudo)spin-valley coupling of Dirac fermions at the zone edges and giant Stark effect. In this talk we will review some of these properties with an emphasis on transition-metal dichalcogenide semiconductors. Finally, we will discuss the potential of these materials within the roadmap for development of nano-electronic devices.

The study of topology in condensed matter is a rapidly growing field.

From classifying the possible topological insulators and superconductors to ab-initio calculations of realizable materials.

In this talk I will use simple language to introduce the subject and survey some recent proposals. In the first part of my talk I will focus on ideas in which a topologically trivial system is driven into a topological phase. In the second part I will discuss the possibility of realizing topological superconductors in two dimensions which support Majorana Fermions in their vortex cores.

תקציר

ההרצאה תכלול את החלקים הבאים:

**1.** תאור המערכת, עקרונות פיזיקליים וטכנולוגיים, דוגמות של פערים קריטיים שפתרנו במשך הפרויקט

ושילוב המערכת בפלטפורמות שונות

**2.** תאור מטריצת ניסויי המערכת: ניסויי המפתח ודוגמאות ניסויים לאישור הביצועים

**3.** היסטורית פיתוח המערכת, חוויות וקשיים בתקופות שונות: תקופת בדיקת ההיתכנות, תקופת המדגים המערכתי,

תקופת פיתוח המערכת המבצעית תקופת ההספקות והוכחת יכולת המערכת בתרחישים מבצעים

In this talk I will discuss how non-abelian anyons that are richer than Majorana fermions may be engineered by coupling counter-propagating edge modes of abelian quantum Hall states. Furthermore, I will discuss whether and when such anyons may be created in one dimensional wires. I will NOT assume that the audience is fluent in the field of non-abelian anyons.

attached

Anyons play an important role in topological quantum computation. They appear as

the natural quasiparticle excitation of fractional quantum Hall states.

At the edge of the two dimensional electron liquid, the excitations

can be described by one dimensional anyons. In this talk I will

present a model for anyonic excitations which is exactly solvable by

Bethe Ansatz, and I will discuss the role of the statistic parameter

in the single component and multicomponent ground state energy.

The inner ear is a remarkable detector of sound waves, sensitive to signals that vary over 3 orders of magnitude in frequencies and 6 orders in pressure. This detection furthermore occurs in a noisy and highly viscous environment, as the sensory cells – the hair cells – are immersed in a fluid compartment, at room temperature or higher. It was proposed that this sensitivity is achieved by poising the system close to a critical point described by a Hopf bifurcation. I present a new model based on a different bifurcation that can likewise act as an amplifier, and compare the performance with previously suggested models as well as with experimental data, obtained both *in vivo *and *in vitro*. This new approach leads to predictions that are in agreement with experiments. In addition, I will demonstrate that ambient noise enhances the detection sensitivity of this mechanism.

*Please not the time change*

In two dimensions, as the microscopic disorder is increased, superconducting films evolve toward an insulating state. This change in ground state has commonly been described as a direct Superconductor–to–Insulator Transition (SIT) and results from the competition between disorder-induced Anderson localization and the formation of a macroscopic superconducting coherent state. a-Nb_{x}Si_{1-x} thin metal–alloy films are a model system to study the influence of disorder on superconductivity through a modification of composition, thickness or annealing. I will first present low temperature DC transport measurements performed on this material. We have evidenced non-predicted dissipative states resulting from the disorder-induced destruction of the superconducting long range order. Second, I will focus on a broadband microwave experimental setup we have developed, and the first measurements we have performed at low temperature to probe the electrodynamicresponse of disordered thin films.

Flat lens concept proposed in 1968 by V.G. Veselago has been mostly investigated in the monochromatic regime. It was recently recognized that the time development of the superlensing effect is yet to be assessed and may spring surprises. Here we extend flat lens focusing to elastic waves in a thin plate. A 45°-tilted square lattice of circular holes drilled in a Duraluminium plate has been chosen to experimentally demonstrate focusing of flexural waves. Lamb wave pulse focusing is achieved below the first stop band. Time-resolved experiments reveal that the focused image shrinks with time below diffraction limit, with a lateral resolution increasing from 1.20 λ to 0.37 λ. Finite-difference time-domain simulations confirm the role in pulse reconstruction of lens resonances which repeatedly self-organize in amplitude and phase to provide with super-oscillations.

Magnetic refrigeration is a promising technology for energy efficient and environmentally friendly cooling. Magnetic refrigeration is based on a fundamental thermodynamic property of magnetic materials: the so-called magnetocaloric effect, which causes a temperature change if the material is subject to an applied magnetic field under adiabatic conditions. This changes of the temperature upon magnetization and demagnetization is used to generate cooling and the magnetocaloric effect is most pronounced in the vicinity of a magnetic phase transition of the material, e.g. from a non-ordered (paramagnetic) to a ferromagnetic state. In the Department of Energy Conversion and Storage, we have been working on magnetic refrigeration since 2001. This presentation focuses on the crucial challenges for the technology: development of magnetocaloric materials, high‐field permanent magnets, and the design and optimization of the entire system. Finally, recent results of our magnetic refrigeration prototype will be presented.

nipr@dtu.dk

Electronic confinement at nanoscale dimensions remains a central means of science and technology. I will describe a novel method for producing electronic nanostructures at the interface between two normally insulating oxides, LaAlO_{3} and SrTiO_{3}. These structures and devices are “written” by a conductive atomic force microscope probe in ambient conditions at room temperature, and can be erased and reconfigured. The spatial dimensions of these structures are comparable to the width of a single-wall carbon nanotube (~2 nm). A wide variety of devices can be created, including nanowires, tunnel junctions, diodes, field-effect transistors, single-electron transistors, superconducting nanowires, quantum dots and nanoscale THz emitters and detectors. This new, on-demand nanoelectronics platform has the potential for widespread scientific and technological exploitation.

Counter propagating (upstream) chiral neutral edge modes, which were predicted to be present in hole-conjugate states, were observed recently in a variety of fractional Quantum Hall States, by measuring charge noise that resulted after partitioning the neutral mode by a constriction. The observation of such modes raised new questions regarding their microscopical nature and the interplay between the charge and neutral edge modes. Moreover, it opened a new way to probe the wave function of the fractional Quantum Hall states at the first excited Landau level, where some states are predicted to be of non-abelian nature.

In this talk, I will present this emerging new field. First I will focus on measurements performed at the ubiquitous *n*=2/3, establishing our measurement techniques and revealing new details on the properties of the neutral modes. Secondly, I will present detailed investigation of the neutral modes at the first excited Landau level, demonstrating the existence of an upstream neutral mode in the n=8/3 and n=5/2 states and excluding its existence at the n=7/3 state. These results supports the non-abelian, anti-pfaffian to be the n=5/2 wave function.

Skyrmions are topologically protected states which are at the focus of considerable theoretical and experimental efforts in recent years. Being originally proposed in the context of particle physics, skyrmions now play a major role in almost every field in physics from condensed matter to cosmology. Particularly they are related to quantum Hall effect and fractional quantum Hall effect, liquid crystals, Bose-Einstein condensates, magnetism and even superconductivity.

We show that dipolar interaction in quasi two dimensional ferromagnetic materials breaks the symmetry between different topological excitations. Being sensitive to long range order the interaction prefers the skyrmion topology with positive winding number over the anti-skyrmion topology with negative winding number. We show that the broken symmetry leads to the occurrence of giant anomalous Hall effect (AHE) due to real-space Berry phase.

Title: "Collective Excitations, Stability of the Excitonic Phase, and Electronic Ferroelectricity in the Extended Falicov--Kimball Model"

Abstract:

We consider the excitonic insulator state (often associated with electronic ferroelectricity), which arises on the phase diagram of an extended spinless Falicov--Kimball model (FKM) at half-filling. Within the Hartree--Fock approach, we calculate the spectrum of low-energy collective excitations in this state up to second order in the narrow-band hopping and/or hybridisation.

This allows to probe the mean-field stability of the excitonic insulator.

The latter is found to be unstable when the case of the pure FKM (no hybridisation with a fully localised band) is approached. The excitonic phase, however, may be stabilised further away from the pure FKM limit. In this case, the low-energy excitation spectrum contains new information about the properties of the excitonic condensate (including the strongly suppressed critical temperature).

Our results on stability and degeneracies of the excitonic insulator phase imply that the presence of both hybridisation and narrow-band hopping is required for electronic ferroelectricity. When only one of these is present, the dielectric constant diverges, yet the electrostatic dipole interactions preclude the formation of spontaneous polarisation.

References: Phys Rev B vol 86, 155134 (2012)

Phys. Status Solidi B vol. 250, p. 557 (2013)

The Kagome Heisenberg antiferromagnet is the most likely candidate for a quantum disordered ground state in two dimensions.

State of the art variational methods on large cylinders found no broken spin or translational symmetries, which defines a "quantum spin liquid".

However little is known about its excitation spectrum, and possible point group symmetry breaking.

Using Contractor Renormalization (CORE) we have recently discovered spectral degeneracies in the large system limit.

These signal the onset of p6 - chirality symmetry breaking in the spin liquid phase.

Experimentally, the p6 chiral order parameter may be detected as a splitting of the optical phonons degeneracy near the zone center.

A scanning probe microscope based on a unique nanoSQUID which is fabricated on the apex of a quartz tip has been developed. The nanoSQUID-on-tip device is fabricated by pulling a quartz tube into a sharp pipette with diameters down to 50 nm followed by deposition of a thin superconducting film onto the sides and the apex of the pipette. The devices operate at 4 K in applied magnetic fields of up to 1T and display an extremely low flux noise. As a result a record spin sensitivity of better than 1 μ_{B}/Hz^{1/2} is achieved that is sufficient for detecting the magnetic moment of a single electron. Using a quartz tuning-fork based AFM technique the nanoSQUID can be scanned few nm above the surface of the sample. The combination of high sensitivity, high spatial resolution, wide bandwidth, and close proximity to the sample opens the pathway to direct investigation and imaging of static and dynamic magnetic phenomena on the nanoscale. Preliminary results of study of vortex dynamics in superconductors and magnetic structures in doped topological insulator will be presented.

We study the effect of an embedded weak scatterer (WS) or a weak link (WL) on the electronic transport in a Luttinger liquid (LL) with interacting electrons coupled to massless bosons (e.g., acoustic phonons). We find that a well-known (for the standard LL) duality relation between scaling dimensions of the electron backscattering in the WS and WL limits, D_ws D_wl = 1, holds in the presence of the additional coupling for an any fixed strength of boson scattering from the impurity. This means that at low temperatures such a system remains either an ideal insulator or an ideal metal, regardless of the scattering strength. On the other hand, when fermion and boson scatterings from the impurity are correlated, the system has a rich phase diagram that includes a metal-insulator transition at some intermediate values of the scattering. The results are translated to a 1D flow of fermion-boson mixture of cold atoms through a constriction.

We study the non-abelian statistics characterizing systems where counter-propagating gapless modes on the edges of fractional quantum Hall states are gapped by proximity-coupling to superconductors and ferromagnets. The most transparent example is that of a fractional quantum spin Hall state, in which electrons of one spin direction occupy a fractional quantum Hall state of $\nu= 1/m$, while electrons of the opposite spin occupy a similar state with $\nu = -1/m$. However, we also propose other examples of such systems, which are easier to realize experimentally. We find that each interface between a region on the edge coupled to a superconductor and a region coupled to a ferromagnet corresponds to a non-abelian anyon of quantum dimension $\sqrt{2m}$. We calculate the unitary transformations that are associated with braiding of these anyons, and show that they are able to realize a richer set of non-abelian representations of the braid group than the set realized by non-abelian anyons based on Majorana fermions. We carry out this calculation both explicitly and by applying general considerations. Finally, we show that topological manipulations with these anyons cannot realize universal quantum computation.

We study transport properties of the helical edge states of 2D integer and fractional

topological insulators (TIs/ FTIs), via one and two constrictions (quantum point

contacts). Such constrictions can be made by adding a gate to the systems where the

coupling between edge states on either side of 2D sample is electronically tuned by this

gate. We study the stability of both the conducting (weak backscattering limit) and

insulating fixed points (weak tunneling limit). Moreover, we explore interesting physics

when double impurity is on resonance, leading to perfect transmission (weak

backscattering limit) and Kondo physics (weak tunneling limit). Using renormalization

group and duality mapping, we analyze phase diagrams for the following cases: (i) single

constriction in FTI, which is a generalization of the single constriction in TIs studied by

J. Teo and C. Kane. (ii) two constrictions in TIs, and (iii) two constrictions in FTIs. We

find different behaviors depending on interaction strength and particularly a regime

where conductance is non-monotonic as a function of temperature in the experimentally

accessible parameter regime.

It is shown that a junction of three quantum Ising chains ($\Delta$-junction) can be described as the 2-channel Kondo model in a box which size is of the order of the Ising model correlation length with spin S=1/2 localized at the junction. The local spin is composed of the zero energy boundary Majorana modes of the Ising models.

Experiments on spins and momentum in quasi one-dimensional structures in the GaAs heterostructure will be described. It will be shown that when the momentum degeneracy is lifted by a source-drain voltage a spontaneous spin polarisation occurs. This polarisation is present when the confinement potential is weakened and electrons can relax and form two rows to minimise repulsion.

The spin polarisation can be further investigated by the focussing of electrons in a weak magnetic field. It is shown that inducing the spin polarisation by lifting the momentum degeneracy gives the same results as a large magnetic field which directly lifts the spin degeneracy.

Cold two-dimensional dipolar fluids are predicted to display a very rich phase diagram and intricate particle correlations in both the classical and quantum regimes, far beyond the well studied weakly interacting gases and are currently a major thrust in modern cold atoms and molecules research.

A dipolar exciton fluid in a semiconductor bilayer is a good system to study such physics directly. Furthermore, these fluids can be transported, controlled, and manipulated over macroscopic distances via their interactions with externally applied potentials, a property that can be utilized for new types of coherent exciton based circuitry on a chip.

I will give an overview of our recent work on dipolar exciton fluids, where we have observed interaction induced particle correlations and a transition from a classical to a quantum many-body fluid, as well as a possible evidence for a sharp macroscopic redistribution with the dark spin states.

I will also present a working multi-functional integrated exciton device, which implements static as well as complex moving external potentials to transport, gate, and route excitonic fluxes over macroscopic distances. This is a proof-of-principle for a building block of an excitonic circuitry.

Controlling the coupling between itinerant electrons and localized spins can lead to exotic magnetic states. A novel model system is the interface between LaAlO3 and SrTiO3, where local magnetic moments are believed to coexist with extended two-dimensional electrons. When the density of the itinerant electrons is tuned above a universal critical density, nc, sub-bands with new orbital symmetries are populated, likely leading to a change in the coupling to the localized spins. In this talk I will present our measurements showing that strong, symmetry-dependent, coupling between itinerant electrons and localized moments leads to an unconventional phase diagram for the LaAlO3/SrTiO3 system. Using anisotropic magnetoresistance and anomalous Hall effect measurements, we identify two phases in the space of carrier density and in-plane magnetic field. At densities n>nc and high fields the system is strongly polarized and shows large crystalline anisotropy. Surprisingly, below a density-dependent critical field which is divergent at nc, the polarization and anisotropy vanish whereas the resistivity sharply rises. This behavior, unobserved in other coupled magnetic systems, could be understood within a model involving a coupling that depends on the symmetry of the itinerant electrons. The interplay between the two phases enables gate-tunable magnetism at the LaAlO3/SrTiO3 interface.

**References**

**424**, 824 (2003).

**101**, 043903 (2008).

**101**, 043903 (2008).

Graphene supports a number of remarkable electronic properties, some

of which make it a candidate for certain microelectronic applications.

The challenge, however, of opening a gap in its electronic spectrum has limited its use for basic

circuit elements such as transistors. In this talk I will review recent work

in which an analog of such a gapped spectrum is induced by a time-dependent potential.

The resulting system turns out to have electronic structure with non-trivial

topology, and is an example of a "Floquet Topological Insulator." It supports

surprising fundamental behaviors -- including a quantized Hall effect with

no magnetic field -- but there are fundamental challenges to predicting its

electronic behavior in settings where it can be measured. I will present

results of numerical calculations in which we meet some of these challenges, and

show what should be found in the simplest possible measurement geometry, a

two-terminal conductor. I will discuss the features of the results that demonstrate

the unusual topology of the electronic structure, as well as surprising properties

that are unique to the time-dependent nature of the system.

Unusual magnetic response of As-deficient iron pnictide LaOFeAs is

discussed. It is shown that As vacancies being nominally non-magnetic

defects induce strong enhancement of paramagnetic response of

nonstoichiometric 1111 iron pnictides. This strong magnetic response

however is not detrimental for superconductivity. The microscopic

theory explaining unconventional properties

of defects in Fe-As planes is based on a generalized Anderson - Wolff

impurity model adapted for multivalley semimetals.

We find a connection between quasicrystals and topological matter, namely establishing that quasicrystals exhibit non-trivial topological phases attributed to dimensions higher than their own. Quasicrystals are materials which are neither ordered nor disordered, i.e. they exhibit long-range order only. Recently, the unrelated discovery of Topological Insulators defined a new type of materials classified by their topology. We show that the one-dimensional Harper and Fibonacci quasicrystals are topologically nontrivial. As a result they exhibit topologically-protected boundary states equivalent to the edge states of the two-dimensional Integer Quantum Hall Effect. Additionally, topological bulk phase transitions occur between topologically nonequivalent quasicrystals. We present experiments using photonic lattices, which harness the resultant boundary phenomena to adiabatically pump light across the quasicrystal, and study the bulk phase transitions using a smooth boundary between different quasicrystals.

In 1981 W.G. Unruh predicted that a thermal spectrum of sound waves would be emitted from the sonic horizon in transonic fluid flow, in analogy to black-hole evaporation. Based on this idea, extended to the realm of nonlinear optics, we explore an optical analogue of the Laval nozzle, in which light propagation through a suitably shaped waveguide, filled with a self-defocusing nonlinear medium, mimics the transonic acceleration of a real fluid expanding through a propulsive exhaust nozzle. Experimental demonstrations of transonic flow in prototype optical nozzles will be presented, and the prospect of observing fluctuations that are classical analogues of Hawking radiation will be discussed.

Thermal and thermoelectric conductivities are ideal probes of interaction effects in

correlated electron systems. This is because, in contrast to an electric current, a heat current can be transmitted also by neutral quasiparticles. For instance, energy can be carried by excitations that mediate interactions between other quasiparticles.

In my talk I will present two examples of the dramatic effect of interactions on thermal and thermoelectric transport phenomena. The first is the Nernst effect in the vicinity of the superconducting phase transition. I will demonstrate that the giant Nernst signal, experimentally observed in amorphous films far above Tc, is caused by the fluctuations of the superconducting order parameter. Moreover, I will discuss the anomalous behavior of the Nernst effect near the magnetic-field-induced quantum critical phase transition. The second example is thermal conductivity in spin liquids. Spin liquids can form in the vicinity of the Mott metal-insulator transition when the charge is gapped while the spin degrees of freedom strongly fluctuate. These low energy excitations, dubbed spinons, can conduct heat. The spinons also exhibit a magnetic interaction that leads to non-Fermi liquid behavior. I will show that even in the absence of disorder this strong interaction provides an efficient relaxation mechanism for heat and spin currents, keeping them finite at the lowest temperatures.

The analogue of friction in fluid dynamics is provided by viscosity, which causes dissipation of the energy of the flow. However, if time reversal symmetry is broken, the viscosity tensor may have non-dissipative components, termed “Hall viscosity”, similarly to the non-dissipative Hall conductivity. The Hall viscosity was shown recently to be topologically-protected in rotationally-invariant systems, and to be equal to half the particle density times the orbital angular momentum per particle. Its observation can therefore be of interest in elucidating the nature of the more exotic quantum Hall filling fractions and related systems (e.g., p+ip superfluids), including the possibility of non-abelian statistics and its use for topological quantum computation. However, no concrete measurement scheme has hitherto been proposed.

With this motivation in mind we developed a microscopic linear response theory of viscosity (dissipative as well as Hall), based on the equivalence between a strain rate and time-dependence of the spatial metric of the system. We applied this formalism to rederive and extend previous results on the Hall viscosity. Furthermore, we have established a general relation between the viscosity tensor and the wave-vector dependent conductivity tensor for Galilean-invariant quantum fluids. This relation enables one to extract the Hall viscosity, as well as other viscosity coefficients (shear and bulk) when relevant, from electromagnetic response measurements.

We show that in disordered ferromagnets, where magnetization reversal involves nucleation, domains’ expansion and annihilation, differences between the time dependencies of these processes are responsible for accumulation of the reversed nuclei, for the asymmetry of forward and backward magnetization reversals and for the respective cumulative growth of hysteresis loops. Presence of dilute enclaves of opposite magnetization within a magnetized ferromagnet can be detected by time and field dependent magnetization reversal. Such enclaves are stable due to dipolar fields generated by the surrounding material, and their presence at the onset of reversal can speed the process by orders of magnitude. The field required to suppress these nuclei and reach true magnetic saturation is found to be an order of magnitude higher than the observable macroscopic saturation field. Fatuzzo – Labrune model is extended to describe magnetization reversal starting with ready nucleation domains.

Majorana qubits in semiconducting wires with strong spin-orbit coupling

.and proximity induced superconductivity are new and promising quantum systems

We study the decoherence of Majorana qubits due the non-adiabatic processes as

.well as the ways to manipulate these qubits non-adiabatically

Topological superconducting wires are predicted to support a localized Majorana bound state at each end. These Majorana states are particle-hole symmetric with a zero excitation energy. Their non-local properties and non-abelian braiding statistics, makes them potentially useful in topological quantum computation schemes. The present wave of interest is driven by a number of proposals that suggest ways of realizing and manipulating Majorana states in solid state systems. One proposal that stands out is the use of semiconductor nanowires with strong spin-orbit interaction that are placed in proximity to s-wave superconductors. Here Majorana manipulation require a mere series of gate operations. In light of these proposals, the experimental observations of zero-bias peaks in normal-metal superconductor tunnel junctions, may indicate the presence of a Majorana bound state. However, for the unambiguous identification of this topologically non trivial state, it is crucial to rule out alternative mechanisms for the zero-bias conductance peak in this apparatus. In the experimental setup the wires are terminated by gate induced potentials which are typically smooth functions of position. We show that even in the topological trivial state such an adiabatic confinement can lead to a fermionic end state with an anomalously small energy. The possible existence of such near-zero-energy levels implies that the mere observation of a zero-bias peak in the tunneling conductance is not an exclusive signature of a topological superconducting phase, even in the ideal clean single channel limit.

In this talk I present a theory of the Coulomb drag effect between two closely positioned graphene monolayers. The interest to the Coulomb drag is motivated by recent experiments with by-layer graphene systems, which use either boron-nitride or aluminium oxide as a spacer. These experiments reveal a strongly non-monotonous dependence of drag resistivity on the electron concentration in graphene. I give a qualitative explanation of the experimental data and discuss the limits of applicability of the Fermi-liquid theory of the Coulomb drag. I also show how to extend the theory to the regime of non-degenerate Fermi liquid which is realized in clean graphene samples doped to a close vicinity of the Dirac point. A further increase in the drag resistivity is predicted in this case.

Recently there is a burst of interest in measurements of interference

patterns and noise of topologically-protected edges states in the quantum

Hall effect regime. One reason for this interest is the potential of these

experiments in demonstrating fractional and non-Abelian statistics between

particles, which may lead to a realization of quantum computation. Another

reason is that a new and diverse group of experiments revealed a non-trivial

influence of the coulomb interactions between electrons on the interference

patterns and on the noise, which we only now begin to understand.

In the talk I will give an overview of the various experiments done in this

research field and the connections between them, and I will outline the

theories which we developed in order to explain their results.

The classical dynamics in stationary potentials that are random both in space and time is studied. It can be intuitively understood with the help of Chirikov resonances that are central in the theory of Chaos, and explored quantitatively in the framework of the Fokker-Planck equation. In particular, a simple expression for the diffusion coefficient was obtained in terms of the average power density of the potential. The resulting anomalous diffusion in velocity is classified into universality classes. The general theory was applied and numerically tested for specific examples relevant for optics and atom optics.

Fractals define a new and interesting realm for a discussion of basic phenomena in QED and

quantum optics and their implementation. This interest results from specific properties of

fractals, e.g., their dilatation symmetry as opposed to the translation symmetry of Euclidean

space and the corresponding absence of Fourier mode decomposition. Moreover, the

existence of a set of distinct (usually non integer) dimensions characterizing the physical

properties (spatial or spectral) of fractals make them a useful testing ground for

dimensionality dependent physical problems.

We shall start by noting that the absence of Fourier transform on a fractal implies necessarily

different notions of volume in direct and reciprocal spaces and thus the need to modify the

Heisenberg uncertainty principle. Implications for field quantization and the definition of the

notion of photon on a fractal will be further addressed.

These ideas will find interesting applications in quantum optics of fractal cavities. More

specifically, we shall discuss the existence of a strong Purcell effect, the modification of

spontaneous emission, and the Casimir effect.

We shall then turn to the case of massive bosons and discuss the nature of Bose-Einstein

condensation and the onset of superfluidity in fractal structures. The existence of distinct

fractal dimensions characterizing spatial and spectral properties is instrumental in

understanding the dimensionality dependence of the BEC and the existence of a superfluid

order either through the existence of an “Off Diagonal Long Range Order” (ODLRO) or the

generalization of the Mermin-Wagner theorem.

We have studied the electron energy loss processes in individual single-walled cnts of very high quality. (1) We are currently conducting studies of Terahertz absorption to find Plasmon spatial resonances of an individual swcnt, to verify the predictions for a Luttinger liquid.(2) We report mechanisms of energy loss and far-infrared absorption. Analogous studies of electron-phonon scattering in graphene have only been reported at high temperatures, or at very high electron densities, ≥ 10^{-13} /cm^{2}. We discuss the prospects for such studies of graphene at lower temperatures and densities.

1. "Energy loss of the electron system in individual single-walled carbon nanotubes," D.F. Santavicca, J.D. Chudow, D.E. Prober, M.S. Purewal and P. Kim, *Nano Lett.* **10**, 4538 (2010); also *Appl. Phys. Lett.* **98**, 223503 (2011), and *APL* to appear (see www.yale.edu/proberlab).

2. “Luttinger Liquid Theory as a model of the Gigahertz Electrical Properties of Carbon

nanotubes” P. J. Burke, IEEE Trans. Nanotech. **1**, p.129 (2002)

The advent of high performance computing and the development of sophisticated numerical techniques have opened new vistas for researchers in condensed matter physics. Exciting predictions of new quantum phases of matter in model systems can often be substantiated or falsified by numerical methods. In this talk, I will present recent development in applying the celebrated density-matrix renormalization–group method to quasi-one dimensional systems. I will show the power of this technique by computing, with high accuracy, critical points in quantum phase transitions induced by small inter-chain interactions. I show that this technique can accurately compute the critical exponent n of the correlation length in the Mott transition. The computed value of n suggest, in agreement with recent slave-rotor speculation, that the Mott transition belongs to the universality class of the classical 3D XY model.

Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral

symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry

classes are random hopping models on bipartite lattices at the band center. As was found by Gade

and Wegner two decades ago within the sigma-model formalism, quantum interference e

ects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum

localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vortex-like excitations of the sigma models. We derive renormalization group equations including these non-perturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically

induced Anderson localization. We also show that the Wess-Zumino and Z2 theta terms on surfaces

of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.

The basic single file process is the diffusion of N (N → ∞) identical Brownian hard spheres in a quasi-one-dimensional channel of length L (L → ∞), such that the spheres do not jump one on top of the other, and the average particle's density is approximately fixed. The most known statistical properties in this process are that the mean square displacement (MSD) of a particle in the file follows, MSD~t1/2 and its probability density function (PDF) is a Gaussian in position with a variance, MSD.

I’LL focus in the talk on three new variants in file dynamics and address the following questions:

(*) First, the question about the origin of the unique scaling, MSD~t1/2, in simple files, is addressed using scaling law analysis and a new approach for full mathematical computations in normal files.

(*) The MSD is derived in normal files with particles’ density that is not fixed and with particles that are not identical, yet, the diffusion coefficients of the particles are distributed according to a probability density function.

(*) Files with anomalous basic dynamics, both renewal ones and those that are not renewal are solved.

We discuss the full counting statistics of charge transport through a nano device and introduce a general way to calculate it numerically at zero-temperature. We apply this to a strongly correlated model: the interacting resonant level model; where it turns out we can also calculate the full counting statistics exactly, to good agreement with the numerics. From the analytic properties of the full solution, we show that the system undergoes charge fractionalization when the bias voltage exceeds a certain threshold.

_{c}versus the strength of the magnetic coupling J, with no other structural changes. We have done this experiment using the (Ca

_{x}La

_{1-x})(Ba

_{1.75-x}La

_{0.25+x})Cu

_{3}O

_{y}system with its 4 different families having different T

_{c}

^{max}, but identical structures. For each family, we measured the Néel

_{N}, the anisotropies of the magnetic interactions, the spin glass temperature T

_{g}of underdoped samples, the carrier density n, the superconducting carrier density n

_{s}, and, of course, T

_{c}from under to overdoped compounds. Our measurements allow us to demonstrate that T

_{c}=cJn

_{s}and more.

We study the topological classification of spin pumps consisting of a family of one-dimensional insulators with a time reversal restriction on the pumping cycle. We find that when adiabatically varied in time, certain band insulators allow for the quantized noiseless pumping of spin even in the presence of strong spin orbit scattering. These spin pumps are closely related to the quantum spin Hall system, and their properties are protected by a time-reversal restriction on the pumping cycle. Based on these findings, we study spin pumps with a bulk energy gap which arises due to electron-electron interactions. We find that the correlated gapped phase can lead to novel pumping properties. In particular, systems with $d$ different ground states can give rise to $d+1$ different classes of spin pumps, including a trivial class which does not pump quantized spin and $d$ non-trivial classes allowing for the pumping of quantized spin $\hbar/n $ on average per cycle, where $1\leq n\leq d$. We discuss an example of a spin pump that transfers on average spin $ \hbar/2$ without transferring charge.

- תאריך עדכון אחרון: 6/11/2017