Related papers: The bulk-edge correspondence for curved interfaces
Bundle gerbes are simple examples of higher geometric structures that show their utility in dealing with topological subtleties of physical theories. I review a recent construction of torsion topological invariants for condensed matter…
By extending the gauge covariant magnetic perturbation theory to operators defined on half-planes, we prove that for $2d$ random ergodic magnetic Schr\"odinger operators, the zero-temperature bulk-edge correspondence can be obtained from a…
Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a…
Bulk boundary correspondence is crucial to topological insulator as it associates the boundary states (with zero energy, chiral or helical) to topological numbers defined in bulk. The application of this correspondence needs a prerequisite…
The centerpiece of topological photonics is the bulk-boundary correspondence principle (BBCP), which relates discrete invariants of the Bloch bands to the possible presence of interface modes between two periodic heterostructures. In…
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making…
We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer…
We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients…
Time-dependent perturbations can drive a trivial two-dimensional band insulator into a quantum Hall-like phase, with protected nonequilibrium states bound to its edges. We propose an experiment to probe the existence of these topological…
We study transport properties of the helical edge states of two-dimensional integer and fractional topological insulators via double constrictions. Such constrictions couple the upper and lower edges of the sample, and can be made and tuned…
Energy dispersion and spin orientation of the protected states at interfaces between topological insulators (TIs) and non-topological materials depend on the charge redistribution, strain, and atomic displacement at the interface. Knowledge…
Edge reconstruction of gate-tunable compressible quantum Hall fluids in the filling fraction range 1/3 to 2/3 is studied by measuring transmitted conductance of two individually excited fractional $e^2/3h$ edge modes of bulk 2/3 fractional…
Topological insulators are bulk semiconductors that manifest in-gap massless Dirac surface states due to the topological bulk-boundary correspondence principle [1-3]. These surface states have been a subject of tremendous ongoing interest,…
Motivated by the recent twisted MoTe$_2$ experiment [arXiv:2601.18508], we develop a disordered interacting edge theory of a fractional topological insulator at $\nu_{\text{tot}}=4/3$, consisting of two time-reversal-conjugated $\nu=2/3$…
The topological insulators have a gap in the bulk but extended states at the edge that can carry current. We study a geometry in which such edge states will manifest themselves through periodic oscillations in the magnetoconductance of a…
Quantum Hall states are characterized by a topological invariant, the many-body Chern number, which determines their quantized Hall conductivity. This invariant also emerges in circular dichroic responses, namely, by applying a circular…
We present a multi-probe transport analysis that effectively separates bulk and edge currents in large Hall bar devices with standard geometries. Applied to transport measurements on all possible four-probe configurations of six-probe Hall…
Three-dimensional topological insulators harbour metallic surface states with exotic properties. In transport or optics, these properties are typically masked by defect-induced bulk carriers. Compensation of donors and acceptors reduces the…
This paper analyzes Floquet topological insulators resulting from the time-harmonic irradiation of electromagnetic waves on two dimensional materials such as graphene. We analyze the bulk and edge topologies of approximations to the…
Topology is bringing new tools for the study of fluid waves. The existence of unidirectional Yanai and Kelvin equatorial waves has been related to a topological invariant, the Chern number, that describes the winding of $f$-plane shallow…