Condensed Matter Resnick seminar

Weyl and nodal line semimetals are classes of three-dimensional quantum 

materials characterized by band degeneracies protected by symmetry and topology. 

In this talk, I explore how magnetic fields induce gap openings in their spectra and 

drive phase transitions through electron tunneling between nodes. We demonstrate 

that external magnetic fields immediately gap the Weyl nodes which is exponentially 

small but finite and significant under certain conditions. For nodal line semimetals, we 

identify a critical Fermi surface area beyond which the system cannot be fully gapped 

by external fields. Additionally, we discuss the conditions under which field-induced 

gapped insulating states exhibit topological nontriviality. Lastly, we introduce straightforward 

diagrammatic rules that reliably predict the topological nature of phases resulting from 

applied magnetic fields. 

Programmable quantum platforms have emerged as powerful tools for studying quantum many-body phenomena in highly entangled systems, with applications ranging from condensed matter and high energy physics to quantum algorithms. In this talk, I will discuss recent developments involving programmable Rydberg atom arrays, which allow for precise and coherent control of hundreds of atoms in two dimensions, along with individual addressability and reconfigurable geometry. First, I will describe explorations of ordering dynamics in a quantum magnet following a quantum phase transition. Using individual atom control, we uncover the interplay of quantum criticality and non-equilibrium phenomena, and observe long-lived oscillations of the order parameter akin to an amplitude (“Higgs”) mode, with interesting implications near the quantum critical point. I will then describe the digital realization of the Kitaev honeycomb model, including observation of an exotic non-Abelian spin-liquid, as well as the use of topological order to design a programmable fermionic simulator. These projects introduce new avenues for the study of quantum criticality and fermionic systems, respectively. Finally, I will briefly discuss future opportunities in explorations of quantum many-body physics with atom arrays, with emphasis on new frontiers in quantum criticality.

Universal behaviors of nonequilibrium quantum many-body systems may be usefully captured by the dynamics of quantum information measures. Notably, the dynamics of bipartite entanglement entropy can distinguish integrable quantum systems from chaotic ones. The two most successful effective theories describing the evolution of entanglement from a low-entangled initial state are the quasiparticle picture and the membrane picture, which provide distinct predictions for integrable and chaotic systems, respectively.

I will present exact results [1] for entanglement dynamics in integrable and chaotic systems perturbed by a quantum impurity, showing that the impurity’s presence strongly alters the growth of entanglement. I will show that in the case of the integrable bulk, a modified version of the integrable quasiparticle picture still holds, despite the impurity generically breaking integrability. On the other hand, the analytical results indicate that for certain chaotic bulk systems, the membrane picture surprisingly fails, pointing to a hitherto unknown gap in its formulation. The exact calculations are facilitated by studying dual-unitary quantum circuits, a class of discrete-time nonequilibrium models that span various types of dynamics while retaining a large degree of analytical solvability.

Finally, I will briefly discuss separate results regarding the interplay between entanglement and impurities in nonequilibrium steady states of free fermion systems [2-5].

[1]          S. Fraenkel and C. Rylands, Entanglement in dual unitary quantum circuits with impurities, arXiv:2410.03442 (2024).

[2]          S. Fraenkel and M. Goldstein, Entanglement measures in a nonequilibrium steady state: Exact results in one dimension, SciPost Phys. 11, 085 (2021).

[3]         S. Fraenkel and M. Goldstein, Extensive long-range entanglement in a nonequilibrium steady state, SciPost Phys. 15, 134 (2023).

[4]         S. Fraenkel and M. Goldstein, Exact asymptotics of long-range quantum correlations in a non-equilibrium steady state, J. Stat. Mech. 2024, 033107 (2024).

[5]         S. Fraenkel and M. Goldstein, Extensive long-range entanglement at finite temperatures from a nonequilibrium bias, Phys. Rev. B 110, 035149 (2024).

Anyons are quasiparticles that obey exchange statistics distinct from those of fermions and  bosons. These exotic particles can be realized within the framework of the fractional quantum Hall effect (FQHE), representing a highly coveted goal in condensed matter physics. In this talk, I will present our group’s recent progress in exploring anyons within bilayer graphene-based van der Waals heterostructures. I will begin by discussing the FQH phase-space in bilayer graphene, highlighting its rich landscape of topological orders, including various non-Abelian states [1]. Following this, I will shift the focus to our interferometry studies at both odd- and even-denominator filling fractions, aimed at detecting the exchange statistics of Abelian and non-Abelian anyons [2,3]. 

[1] R. Kumar, A. Haug, et al., Quarter- and half-filled quantum Hall states and their competing interactions in bilayer graphene, arXiv: 2405.19405
[2] J. Kim, H. Dev, et al., Aharonov–Bohm interference and statistical phase-jump evolution in fractional quantum Hall states in bilayer graphene, Nature Nanotechnology 19, 1619-1626 (2024)
[3] J. Kim, H. Dev, et al., Aharonov-Bohm Interference in Even-Denominator Fractional Quantum Hall States, arXiv: 2405.19405

The electron-electron and electron-phonon coupling in complex materials can be more complicated than simple density-density interactions, involving intertwined dynamics of spin, charge, and spatial symmetries. This motivates studying universal models with complex interactions and whether BCS-type singlet pairing is still the “natural” fate of the system. To this end, we construct a Yukawa-SYK model with nonlocal couplings in both spin and charge channels. Furthermore, we provide for time-reversal-symmetry breaking dynamics by averaging over the Gaussian unitary ensemble rather than the orthogonal ensemble. We find that the ground state of the system can be an orbitally nonlocal superconducting state arising from incoherent fermions with no BCS-like analog. The superconductivity has an equal tendency to triplet and singlet pairing states separated by a non-Fermi liquid phase. We further study the fate of the system within the superconducting phase and find that the expected ground state, away from the critical point, is a mixed singlet/triplet state. Finally, we find that, while at 𝑇𝑐 the triplet and singlet transitions are dual to one another, below 𝑇𝑐 the duality is broken, with the triplet state more susceptible to orbital fluctuations just by its symmetry. Our results indicate that such fluctuation-induced mixed states may be an inherent feature of strongly correlated materials.

Hybrid interfaces, a boundary between solid (such as metals or semiconductors) and molecule, play an essential role in determining the physical properties (optoelectronics and Magnetics) of the material. For example, it is important in electronics to control parameters such as work function and band banding, while in photonics, such as plasmonic nanostructures, it is fundamental to control field enhancement. Another example relzted to magnetics, we can shift a diamgenic surface to ferromagnetic by dipole molecules.To this end, selecting the proper molecule for a particular application and designing the interface's architecture is crucial. The hybrid interfaces are relzied by molecular termination.  The interface characterization is based on on x-ray photoelectronic spectroscopy, Raman, Kelvin probe, surface photovoltage and Magnetc Force-Microscopy. The experimental results are supported with a simulation.  

The study of light dynamics in the frequency domain has been pivotal for applications in metrology and communications. One of the most impactful states is the optical frequency comb—a broadband light state where frequencies are equally spaced. To generate these combs, we rely on two key processes: nonlinear frequency proliferation and stabilization. When frequency proliferation occurs inside multimode lasers, the gain recovery time emerges as a critical factor for stabilization. Over 40 years ago, the stabilization process was described by slow and selective dissipation, like gain curvature in frequency or gain modulation in time [1]. However, recent advances in semiconductor-based frequency-comb sources have shown that when the gain recovery time becomes very short [2], the dynamics of light in the frequency domain becomes radically different [3-6].

In my talk, I will present the exploration of light dynamics in a discrete frequency space, when gain recovery times are fast [7,8]. I will show that light traveling through a medium with fast gain saturation transforms it into a type of liquid, which forces coherent dynamics despite destabilization processes, for example quenching or dephasing. This liquid state of light allows to explore fully the synthetic lattice in the frequency space, reaching its maximal limit given by the linear system. Such a platform not only advances our understanding of quench dynamics in non-equilibrium systems, but can also lead to innovative quantum inspired devices, like the recently discovered quantum walk comb source [7].

References

[1] H. Haus, “A theory of forced mode locking” IEEE J. Quantum Electron. 11, 323–330 (1975).

[2] U. Senica, A. Dikopoltsev, et al., “Frequency-Modulated Combs via Field-Enhancing Tapered Waveguides”, Laser Photonics Rev, 2300472 (2023).

[3] J. B. Khurgin, et al. "Coherent frequency combs produced by self frequency modulation in quantum cascade lasers." APL 104.8 (2014).

[4] N. Opačak, et al., “Theory of frequency-modulated combs in lasers with spatial hole burning, dispersion, and Kerr nonlinearity” Phys. Rev. Lett. 123, 243902 (2019).

[5] D. Burghoff, "Unravelling the origin of frequency modulated combs using active cavity mean-field theory." Optica 7.12 (2020): 1781-1787.

[6] M. Piccardo, et al. "Frequency combs induced by phase turbulence." Nature 582.7812 (2020): 360-364.

[7] I. Heckelmann*, M. Bertrand*, A. Dikopoltsev*, et al., “Quantum walk comb in a fast gain laser”, Science 382, 434-438 (2023).

[8] A. Dikopoltsev, et al. "Quench dynamics of Wannier-Stark states in an active synthetic photonic lattice." arXiv:2405.04774 (2024).

Magnetism emerges from the electronic interactions between the neighboring atoms. In confined samples, the proportion of atoms near the surface is larger. Surface atoms have fewer neighbors and, thus, are expected to exhibit weaker magnetic correlations than the ones inside a bulk sample. In this work, we employ a magnetic imaging technique^[1,2], which unveils a material, CrGeTe₃, where we observe the opposite effect. In relatively thick samples (d>10 nm), we observe that only the edge of the sample remains magnetized at zero applied field^[3]. We show that two nearby edges stabilize the magnetism in the region between the edges, resulting in a quasi-1D magnetic structure^[4]. Such proximity effect is observed down to the zero-dimension limit (nanoisland). In such a limit, we can create an array of magnetic nanoparticles of different aspect ratio. The particle coercive field shows anomalous scaling as a function of dimensions, which we interpret as another evidence of the edge effect in CrGeTe₃.

[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, E. Zeldov, Nat. Nanotechnol. 2013, 8, 639.

[2]         Y. Anahory, H. R. Naren, E. O. Lachman, S. Buhbut Sinai, A. Uri, L. Embon, E. Yaakobi, Y. Myasoedov, M. E. Huber, R. Klajn, E. Zeldov, Nanoscale 2020, 12, 3174.

[3]         A. Noah, H. Alpern, S. Singh, A. Gutfreund, G. Zisman, T. D. Feld, A. Vakahi, S. Remennik, Y. Paltiel, M. E. Huber, V. Barrena, H. Suderow, H. Steinberg, O. Millo, Y. Anahory, Nano Lett. 2022, 22, 3165.

[4]         A. Noah, Y. Zur, N. Fridman, S. Singh, A. Gutfreund, E. Herrera, A. Vakahi, S. Remennik, M. E. Huber, S. Gazit, H. Suderow, H. Steinberg, O. Millo, Y. Anahory, ACS Appl. Nano Mater. 2023, 6, 8627.

The Anderson localization transition in quantum graphs has garnered significant recent attention due to its relevance to many-body localization studies. Typically, graphs are constructed using top-down methods. Here, we explore a bottom-up approach, employing a simple local rewriting rule to construct the graph. Through the use of ratio statistics for the energy spectrum and Kullback-Leibler divergence correlations for the eigenstates, numerical analysis demonstrates that slight adjustments to the rewriting rule can induce a transition from a localized to an extended quantum phase. This extended state exhibits non-ergodic behavior, akin to the non-ergodic extended phase observed in the Porter-Rosenzweig model and suggested for many-body localization. Thus, by adapting straightforward local rewriting rules, it becomes feasible to assemble complex graphs from which desired global quantum phases emerge. This approach holds promise for numerical investigations and could be implemented in building optical realizations of complex networks using optical fibers and beam splitters.

Anharmonic lattice vibrations play a key role in many physical phenomena. They govern the heat conductivity of solids, strongly affect the phonon spectra, play a prominent role in soft mode phase transitions, allow ultrafast engineering of material properties, and more. The most direct evidence for anharmonicity is to measure the oscillation frequency changing as a function of the oscillation amplitude. For lattice vibrations, this is not a trivial task, and anharmonicity is probed indirectly through its effects on thermodynamic properties and spectral features or through coherent decay of one mode to another. However, measurement of the anharmonicity of a single Raman mode is still lacking. We show that ultrafast double pump-probe spectroscopy could be used to directly observe frequency shifts of Raman  phonons as a function of the oscillation amplitude and disentangle contributions from quasi-harmonic sources such as temperature and changes to the carrier density in the thermoelectric material SnTe. Our results have dramatic implications for the material engineering of future thermoelectrics. Moreover, our methodology could be used to isolate the basic mechanisms driving optically induced phase transitions and other nonlinear phenomena.

Recent experiments in superconducting circuits have demonstrated the high probability splitting of single-photons [1,2], a phenomenon rarely observed in nature. This exotic effect is enabled by a high-impedance Josephson transmission line which increases the effective coupling of the microwave photons to an artificial atom, and provides a useful tool to probe fundamental phenomena in many-body systems.
I will discuss a collaboration with the Manucharyan and Kuzmin groups, in which we utilized single-photon splitting to observe the Schmid-Bulgadaev quantum phase transition [3], whose lack of clear evidence has sparked a recent debate. The experimental system realizes the boundary sine-Gordon model, which is known to be integrable and is characterized by purely elastic scattering of elementary excitations, that seems at odds with photon splitting. I will show that a nonlinear relation between these excitations and the photons not only allows for inelastic decay of the latter, but also that integrability provides powerful analytical tools yielding exact results for the total inelastic decay rate and the spectrum of the resulting photons [4]. Our results shed light on the Schmid-Bulgadaev transition, and compare nicely with experimental measurements.

References:

[1] R. Kuzmin, N. Grabon, N. Mehta, A. Burshtein, M. Goldstein, M. Houzet, L. I. Glazman, and V. E. Manucharyan, "Inelastic scattering of a photon by a quantum phase slip", PRL 126 197701 (2021)

[2] A. Burshtein, R. Kuzmin, V. E. Manucharyan, and M. Goldstein, "Photon-instanton collider implemented by a superconducting circuit", PRL 126 137701 (2021)

[3] R. Kuzmin, N. Mehta, N. Grabon, R. A. Mencia, A. Burshtein, M. Goldstein, and V. E. Manucharyan, "Observation of the Schmid-Bulgadaev dissipative quantum phase transition", arXiv:2304.05806, accepted to Nature Physics (2024)

[4] A. Burshtein and M. Goldstein, "Inelastic decay from integrability", PRX Quantum 5 020323 (2024)

We study ground states of SU(4) quantum antiferromagnets on the triangular lattice that arise from Mott-insulating phases of fermions with four flavors. We consider different fillings of the SU(4) fermions, which lead to different representations of SU(4) on each site.

For the case of a single fermion per site, corresponding to the fundamental representation of SU(4), we carry out a variational Monte Carlo (VMC) study uncovering a novel candidate for the ground state of the system. This state features simultaneous breaking of SU(4) flavor symmetry down to SU(3)×U(1) along with bond trimerization. We illuminate our findings by considering a mapping to an effective model of SU(4) spins on the honeycomb lattice with a fundamental - anti-fundamental representation on the two sublattices. We show that the SU(4)-broken state on the triangular lattice maps to a flavor-antiflavor Néel ordering on the honeycomb lattice.

In the case of two fermions per site, which corresponds to the self-conjugate representation of SU(4), we study the bilinear-biquadratic antiferromagnetic model. Considering an effective dimer model, we show that for a finite range of biquadratic couplings the system resides in the RVB spin liquid phase.

 I will talk about the properties of microscopical models of one-dimensional topological insulators in universality classes that possess chiral symmetry.  To construct such models we start with a deformation of the Su-Schrieffer-Heeger chain that breaks time-reversal symmetry, which puts it in the AIII class that has chiral symmetry only. We then couple this model to its time-reversal counterpart to build models in other symmetry classes [1]. This construction is similar to what has been done by Kane and Mele in their construction of Spin Hall insulator by coupling two Quantum Hall planes. I will talk about topological properties of such models, and in particular, will demonstrate that the models that belong to Z classes can be adiabatically deformed into one another without the change of topological invariant as long as chiral symmetry is preserved. This property is general and holds also in three dimensions [2].  I will also discuss how interactions change the topological properties of the constructed models by using bosonisation [3]. 

[1]  P. Matveeva, T. Hewitt, D. Liu, K. Reddy, D. Gutman, and S. T. Carr, Phys. Rev. B 107, 075422 (2023) 

[2] D. Liu, P. Matveeva, D. Gutman, S.T. Carr , Phys.Rev. B 108 (3), 035418 (2023)

[3] P. Matveeva, D. Gutman, and S. T. Carr, Phys. Rev. B 109, 165436 (2024)

Electron correlation is responsible for numerous intriguing condensed matter phenomena, such as metal-insulator transitions, ferroelectricity, colossal magnetoresistance, 2D electron gases, and high-temperature superconductivity. Perovskite oxides serve as an attractive testbed for many of these phases, arising from the intricate interplay of spin, orbital, lattice, and charge degrees of freedom. One of the grand challenges in this field is understanding how strong quantum many-body interactions affect the electronic structure of these materials and ultimately lead to these exotic properties. In pursuit of this goal, researchers are increasingly focusing on the design and synthesis of artificial heterostructures, which offer new ways to tune material parameters and endow these systems with novel properties. I will present our recent studies of the alkaline earth stannates, particularly BaSnO3, which demonstrate light transparency and high electrical conductivity when doped. By combining thin film growth, angle-resolved photoemission spectroscopy, and ab initio calculations, we reveal the existence of a 2-dimensional metallic state at the SnO2-terminated surface of a 1% La-doped BaSnO3 thin film. This surface state is characterized by a distinct carrier density and a smaller effective mass compared to the corresponding bulk values. The small effective mass of the surface state, about 0.12me, indicates that BSO can be a crucial component in transition metal oxide heterostructures with significantly improved electrical conductivity.

If time permits, I will also present our recent work on synthesizing infinite-layer nickelates that exhibit unconventional superconductivity. Our angle-dependent anisotropic magnetoresistance measurements have provided crucial insights into the evolution of magnetic ordering from the parent compound phase to the superconducting state. The results suggest a similarity between superconducting nickelates and electron-doped cuprates.

De Haas-van Alphen quantum oscillations in magnetization have traditionally served as the prime tool for determining the band structure of metals and semiconductors. Utilizing a scanning SQUID-on-tip, we image thermodynamic quantum oscillations with nanoscale spatial resolution and at very low magnetic fields, offering a novel powerful tool for reconstruction of the local band structure with high energy resolution. In Bernal-stacked trilayer graphene with dual gates, we reconstruct the band structure and its controllable evolution with the displacement field with unprecedented precision, and map the naturally occurring strain-induced pseudomagnetic fields as low as 1 mT, corresponding to graphene twisting by 1 millidegree over 1 µm distance [1]. In Bernal bilayer graphene aligned to hBN, we reveal complex band structure with narrow moiré bands and multiple overlapping Fermi surfaces separated by very small momentum gaps. In addition to conventional oscillations obeying Onsager quantization, pronounced quantum oscillations are found to arise from particle-hole superposition states induced by coherent magnetic breakdown [2]. In twisted trilayer graphene, we observe doping-dependent renormalization of the single-particle band structure by Coulomb interactions, greatly increasing the bandwidth of the flat bands and leading to symmetry breaking at half filling. On approaching charge neutrality, we find the ground state to be a nematic semimetal in which the flat-band Dirac cones migrate towards the mini-Brillouin zone center due to exchange interactions, spontaneously breaking the C3 rotational symmetry [3].

1. H. Zhou, N. Auerbach, M. Uzan, Y. Zhou, N. Banu, W. Zhi, M. E. Huber, K. Watanabe, T. Taniguchi, Y. Myasoedov, B. Yan, and E. Zeldov, “Imaging quantum oscillations and millitesla pseudomagnetic fields in graphene”, Nature 624, 275 (2023).
2. M. Bocarsly, M. Uzan, I. Roy, S. Grover, J. Xiao, Z. Dong, M. Labendik, A. Uri, M. E. Huber, Y. Myasoedov, K. Watanabe, T. Taniguchi, B. Yan, L. S. Levitov, and E. Zeldov, “De Haas–van Alphen spectroscopy and magnetic breakdown in moiré graphene”, Science 383, 42 (2024).
3. M. Bocarsly, I. Roy, V. Bhardwaj, M. Uzan, P. Ledwith, G. Shavit, N. Banu, Y. Zhou, Y. Myasoedov, K. Watanabe, T. Taniguchi, Y. Oreg, D. Parker, Y. Ronen, and E. Zeldov, unpublished.

TBA

The coexistence of multiple types of orders is a common theme in condensed matter physics and unconventional superconductors. Understanding the nature of superconducting orders can be achieved by examining local perturbations such as vortices. For thin films, the vortex magnetic profile is characterized by the Pearl length (Λ), which is inversely proportional to the 2D superfluid density and typically inversely proportional to the film thickness (d).

In Yonathan Anahory’s lab, scanning SQUID-on-tip microscopy has been employed to measure Λ in NbSe2 flakes with thicknesses ranging from 3 to 53 layers. For thicknesses greater than 10 layers, the expected relationship (Λ ∝ 1/d) is observed. However, in six-layer films, Λ exhibits a sharp increase, deviating by a factor of three from the anticipated value. Interestingly, this deviation remains constant for films with 3 to 6 layers. This anomalous behavior suggests the competition between two distinct orders: one present only on the first and last layers of the film, and the other existing throughout all layers.

In this talk, I will begin by reviewing the theory of Pearl vortices. Subsequently, I will present the experimental data and introduce a phenomenological model that explains these observations.

Quantum ferroelectric metals offer a fascinating window into the dynamical processes that give rise to inversion symmetry breaking in quantum materials. At the same time, they constitute an extremely promising platform for future quantum applications. I will describe a recent theoretical attempt to describe the ferroelectric quantum critical point in such systems, and share some insights about what makes the ferroelectric transition unique in the landscape of symmetry-breaking phenomena in correlated electron systems. Finally, I will discuss our current understanding of superconducting strontium titanate and its relation to ferroelectric quantum criticality.

The recent discovery of interaction-driven viscous electronic hydrodynamics in graphene has inspired new devices and insights about other materials. In this new regime, the well-known rules of Ohmic transport no longer apply, and a number of effects have been identified in electronic transport. Despite these advancements, the hydrodynamic analogue of Joule heating remains unexplored, and the thermal properties of hydrodynamic electronic devices are unknown. In this work, we probe graphene hydrodynamics with thermal transport and find two distinct, qualitative signatures: thermal conductivity suppression below the Wiedemann-Franz value and negative thermal magnetoresistance.

These signatures arise from two distinct aspects of this new regime: microscopic momentum conservation due to electron-electron scattering,and geometry-dependent viscous dissipation. We find they are coincident in temperature and density, providing new and robust qualitative signatures of hydrodynamics in a simple, two-terminal global transport setup. Our results mark the first observation of viscous electronic heating in an electron fluid, which may influence the design of hydrodynamic devices and offers a new methodology to identify hydrodynamic states in other systems.

Measurement induced entanglement phase transitions (MIPT) are a class of recently discovered theoretical dynamical transitions in quantum many-body systems, in which a unitary quantum circuit's evolution is interspersed with measurements. The unitary dynamics competes against the localization of the wavefunction due to repeated measurements, resulting in a transition from the quantum entangled (volume-law) phase into a disentangled Zeno-like (area-law) phase at strong measurements, that’s unsuitable for further quantum operations. Recently an extended critical phase with a logarithmic scaling of the entanglement entropy has been identified in a class of integrable models with dissipative dynamics. We extend this and study the critical transition in a non-integrable system - a one dimensional transverse field Ising model, in presence of an integrability-breaking field and no-click dissipation. First, we show that the measurement induced transitions in this system is qualitatively different from the trivial volume-law to area-law transition of the entanglement entropy in integrable systems. Then we show how these transitions can be connected via the integrability breaking field. We also identify the same phase transitions from the correlation function exponents in each phase, and present the complete phase diagram for this non-integrable system.

Recent experimental studies of strongly disordered Indium Oxide films revealed an unusual first-
order quantum phase transition between superconducting and insulating state (SIT), with the jump
between nonzero and zero values of superfluid stiffness at the transition arXiv:2404.09855 . This finding is in sharp contradiction with a ”scaling scenario” discussed usually in relation to SIT. In the present paper we propose a simple theory of this first-order transition. It is based upon idea of competition between two intrinsically different ground states that can be formed by initially localized (due to strong
disorder) electron pairs: superconducting state and Coulomb glass insulator. These two ground
states are characterized by two crucially different order parameters, thus it is natural to expect
a discontinuous transition between them at T = 0. The transition happens when magnitudes of
superconducting gap ∆ and Coulomb gap EC are comparable. We also extend our analysis to
low nonzero temperatures and provide a mean-field ”phase diagram” in the plane (T /∆, EC /∆).
Our results demonstrate the existence of natural upper bound for kinetic inductance of a strongly
disordered superconductor.

The fractional quantum Hall effect, first observed some four decades ago,  is a system where Anyons - particles of fractional charges and fractional quantum statistics - flourish. In the last year, several important developments have brought the physics of Anyons back into the limelight. In particular, Anyons were shown to be quantum particles that can interfere as waves, and their traditional "alma mater", the fractional quantum Hall effect, has been shown to exist even without the application of any magnetic field.

I will review some of these developments, focusing on the theory behind them, and making minimal assumptions of prior knowledge.

 Berry phases strongly affect the properties of crystalline materials, giving rise to modifications of the semiclassical equations of motion that govern wave-packet dynamics. In non-Hermitian systems, generalizations of the Berry connection using the bi-orthogonal formalism have been argued to characterize the topology of these systems. Since non-Hermitian Hamiltonians could be relevant for many types of open and lossy systems it is important to understand how these new quantities enter equations of motion for semi-classical wavepackets. Since generally for non-Hermitian systems the adiabatic theorem fails, this poses a challenge to the theory. I will discuss how to define observables and the conditions under which we can still apply the single band limit, and introduce the type of anomalous terms that may appear in the equation of motion and are present already in one-dimensional systems. I will also discuss the conditions for observing these anomalous contributions and potential extensions of the formalism to include complex electric fields, and magnetic fields.

Boundary-induced electronic phenomena (edge-physics) play a crucial role in explaining the fundamental mechanism driving conductivity in exotic material systems where conventional band theory predicts a nonmetallic phase, advancing applicative quantum materials research. Yet despite a decade of scientific advancement in this field, limited layered material systems have been demonstrated to exhibit edge states, and the harnessing of such states for technological device applications remains challenging. In this talk, I will show experimental evidence for the emergence of confined-edge current flow rising from the Commensurate Charge Density Wave (CCDW) phase of the Van der Waals material 1T-TaS₂. Through the fabrication and conductance analysis of meso-scale 1T-TaS₂ crossbar devices we demonstrate the ability to toggle between high and low resistance states via anisotropic write currents. By spatially mapping the current density via scanning SQUID microscopy, we reveal the current density path in the low-resistance conduction state resides dominantly along the device edges. Surprisingly, the edge flow is confined to a single side of the device which selects a preferable edge and can be manipulated. This single confined edge current flow, which can be explained by CDW domain-wall or CDW single domain formation, raises many question regarding its nature and possible applications of confined current manipulation.

Discrete and local responses of crystalline matter structures are pivotal elements facilitating the ongoing information revolution. A direct way to switch the properties and response of a given structure is to modify its crystalline symmetries by changing the relative atomic positions. Structural rearrangements, however, are challenging due to the solid interatomic bonds involved, which limits current technologies to alternating electronic orders without moving the atoms.

Interestingly, recent experiments show efficient control of atomic scale shifts in layered 2D crystals along their van der Waals (vdW) interfaces. The layers exhibit discrete sliding steps between meta-stable crystalline configurations in response to external electric fields or stress. These 2D vdW polytypes include periodic configurations that preserve substantial interlayer band hybridizations with distinct structural symmetries and diverse electronic/optical/magnetic properties. Their local switching occurs via mobile incommensurate partial dislocations lines, free to slide in a super-lubricant manner to replace one polytype with another.

The talk will outline the many possible polytypes in mono and binary compounds, their typical stacking energies, orbital inter-layer overlaps, and discrete symmetries. Following that, I will discuss the corresponding response of each polytype, including its internal charge redistribution, electric polarization, and underlying band structure. I will emphasize our recent reports of interfacial ferroelectricity [1], ladder-like cumulative polarization [2], doping-dependent polarization in elemental graphitic polytypes [3], and the microscopic dynamics of dislocation boundary lines between polytypes. Finally,  we will discuss opportunities to extend this conceptual "slide-tronics" switching mechanism to efficient swapping between structural symmetries and orientations that should turn Sliding vdW Polytypes into a vast field of research.

1. "Interfacial ferroelectricity by van-der-Waals sliding"

https://www.science.org/doi/10.1126/science.abe8177

2. "Cumulative Polarization in Conductive Interfacial Ferroelectrics"

https://www.nature.com/articles/s41586-022-05341-5

3. "Spontaneous Electric Polarization in Graphene Polytypes"

https://arxiv.org/abs/2305.10890