# Condensed Matter Resnick seminar

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-TaS_{2}. Through the fabrication and conductance analysis of meso-scale 1T-TaS_{2} 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.

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

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

- "Cumulative Polarization in Conductive Interfacial Ferroelectrics"

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

- "Spontaneous Electric Polarization in Graphene Polytypes"

https://arxiv.org/abs/2305.10890