Related papers: The Bulk-Edge Correspondence in Three Simple Cases
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry.…
Seeking the criterion for diagnosing topological phases in real materials has been one of the major tasks in topological physics. Currently, bulk-boundary correspondence based on spectral measurements of in gap topological boundary states…
A scenario of non-Hermitian bulk--boundary correspondence proposed for one-dimensional topological insulators is adapted to a non-Hermitian Chern insulator to examine its applicability to two-dimensional systems. This scenario employs bulk…
Topological insulators feature a number of topologically protected boundary modes linked to the value of their bulk invariant. While in one-dimensional systems the boundary modes are zero dimensional and localized, in two-dimensional…
Transfer matrix methods and intersection theory are used to calculate the bands of edge states for a wide class of periodic two-dimensional tight-binding models including a sublattice and spin degree of freedom. This allows to define…
In this manuscript, we study the interplay between symmetry and topology with a focus on the $Z_2$ topological index of 2D/3D topological insulators and high-order topological insulators. We show that in the presence of either a…
In this work, we study the disorder effects on the bulk-boundary correspondence of two-dimensional higher-order topological insulators (HOTIs). We concentrate on two cases: (i) bulk-corner correspondence, (ii) edge-corner correspondence.…
More profound than bulk topological order of quantum materials is only its unwinding via gapless excitations along boundaries of the sample. We recast this bulk-edge correspondence -- for the experimentally relevant case of fractional…
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…
Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which…
Topological edge modes are excitations that are localized at the materials' edges and yet are characterized by a topological invariant defined in the bulk. Such bulk-edge correspondence has enabled the creation of robust electronic,…
The bulk-edge correspondence (BEC) is the hallmark of topological systems. In continuous (nonlattice) Hermitian systems with an unbounded wave vector, it was recently shown that the BEC of Chern insulators is modified. How would it be…
The bulk-boundary correspondence guarantees topologically protected edge states in a two-dimensional topological superconductor. Unlike in topological insulators, these edge states are, however, not connected to a quantized (spin) current…
In the context of topological insulators, the shallow-water model was recently shown to exhibit an anomalous bulk-edge correspondence. For the model with a boundary, the parameter space involves both longitudinal momentum and boundary…
We study three dimensional systems where strong repulsion leads to an insulating state via spontaneously generated spin-orbit interactions. We discuss a microscopic model where the resulting state is topological. Such topological `Mott'…
A weak topological insulator in dimension $3$ is known to have a topologically protected gapless mode along the screw dislocation. In this paper we formulate and prove this fact with the language of C*-algebra K-theory. The proof is based…
Recently, there is an interest in studying the bulk-edge correspondence for nonlinear eigenvalues problems in a two-dimensional topological system with spin-orbit coupling. By introducing auxiliary eigenvalues, the nonlinear bulk-edge…
We propose an unconventional bulk-edge correspondence for two-dimensional Stiefel-Whitney insulators and Euler insulators, which are topological insulators protected by the $PT$ symmetry. We find that, although the energy spectrum under the…
We focus on a scenario of non-Hermitian bulk--boundary correspondence that uses a topological invariant defined in a bulk geometry under a modified periodic boundary condition. Although this has succeeded in describing the topological…
Topology in condensed matter physics manifests itself in the emergence of edge or surface states protected by underlying symmetries. We review two-dimensional topological insulators whose one-dimensional edge states are characterized by…