Related papers: Bulk-Edge Correspondence for Finite Two-dimensiona…
We introduce an effective edge network theory to characterize the boundary topology of coupled edge states generated from various types of topological insulators. Two examples studied are a two-dimensional second-order topological insulator…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems…
We analyze the disorder driven localization of the two dimensional Bose-Hubbard model by evaluating the full low energy quasiparticle spectrum via a recently developed fluctuation operator expansion method. For any strength of the local…
We show that the bulk-edge correspondence for two-dimensional type A and type AII topological insulators follows directly from the cobordism invariance of the index.
Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological…
According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines topological order in the gapped bulk. As the bulk is less accessible, the last two decades saw the emergence of…
We investigate a two-dimensional superconducting system with a smoothly and periodically varying order parameter. The order parameter is modulated along one direction while remaining uniform in the perpendicular direction, leading to a…
Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…
In this note, we prove the equality of the quantum bulk and the edge Hall conductances in mobility edges and in presence of disorder. The bulk and edge perturbations can be either of electric or magnetic nature. The edge conductance is…
The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under…
The bulk-edge correspondence is one of the most important ingredients in the theory of topological phases of matter. While the bulk-edge correspondence is applicable for Hermitian junction systems where two subsystems with independent…
The same bulk two-dimensional topological phase can have multiple distinct, fully-chiral edge phases. We show that this can occur in the integer quantum Hall states at $\nu=8$ and 12, with experimentally-testable consequences. We show that…
Bulk-edge correspondence is a cornerstone in topological physics, establishing a connection between the number of unidirectional edge modes in physical space and a Chern number, an integer that counts phase singularities of the eigenmodes…
In topological phases of matter for which the bulk and boundary support distinct electronic gaps, there exists the possibility of decoupled mobility gaps in the presence of disorder. This is in analogy with the well-studied problem of…
Quantum Hall systems are characterized by the quantization of the Hall conductance -- a bulk property rooted in the topological structure of the underlying quantum states. In condensed matter devices, material imperfections hinder a direct…
The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose…
We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the…
Recently, several authors have investigated topological phenomena in periodically-driven systems of non-interacting particles. These phenomena are identified through analogies between the Floquet spectra of driven systems and the band…
Using the Laughlin's argument on a torus with two pin-holes, we numerically demonstrate that the discontinuities of the center-of-mass work well as an invariant of the pumping phenomena during the process of the flux-attachment, trading the…