Related papers: Proof of bulk-edge correspondence for band topolog…
We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…
Topological insulators can be characterized alternatively in terms of bulk or edge properties. We prove the equivalence between the two descriptions for two-dimensional solids in the single-particle picture. We give a new formulation of the…
We provide an elementary proof and refinement of a well-known idea from physics: a chiral-symmetric local Hamiltonian on a half-space has the same signed number of edge-localized states with energies in the bulk band gap, as its bulk…
Bulk-edge correspondence is one of the most distinct properties of topological insulators. In particular, the 1D winding number $\n$ has a one-to-one correspondence to the number of edge states in a chain of topological insulators with…
The bulk-edge correspondence is a fundamental principle of topological wave physics, which states that the difference in gap Chern numbers between the interfaced materials is equal to the net number of topological edge modes. Although this…
We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…
The bulk-boundary correspondence, a topic of intensive research interest over the past decades, is one of the quintessential ideas in the physics of topological quantum matter. Nevertheless, it has not been proven in all generality and has…
With the inclusion of arbitrary long-range hopping and (pseudo)spin-orbit coupling amplitudes, we formulate a generic model that can describe any two-dimensional two-band bulk insulators, thus providing a simple framework to investigate…
A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting…
We study one-dimensional insulators obeying a chiral symmetry in the single-particle picture. The Fermi level is assumed to lie in a mobility gap. Topological indices are defined for infinite (bulk) or half-infinite (edge) systems, and it…
In this paper, we rigorously prove the bulk-edge correspondence for finite two-dimensional ergodic disordered systems. Specifically, we focus on the short-range Hamiltonians with ergodic disordered on-site potentials. We first introduce the…
In this paper, we introduce a variation of the notion of topological phase reflecting metric structure of the position space. This framework contains not only periodic and non-periodic systems with symmetries in Kitaev's periodic table but…
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern…
In this work, we establish the bulk-edge correspondence principle for finite two-dimensional photonic structures. Specifically, we focus on the divergence-form operator with periodic coefficients and prove the equality between the…
The bulk-edge correspondence links the Chern-topological numbers with the net number of unidirectional states supported at an interface of the relevant materials. This fundamental principle is perhaps the most consequential result of…
A 2-torsion topological phase exists for Hamiltonians symmetric under the wallpaper group with glide reflection symmetry, corresponding to the unorientable cycle of the Klein bottle fundamental domain. We prove a mod 2 twisted Toeplitz…
We present examples in three symmetry classes of topological insulators in one or two dimensions where the proof of the bulk-edge correspondence is particularly simple. This serves to illustrate the mechanism behind the bulk-edge principle…
We develop a formalism to extend, simultaneously, the usual definition of bulk and edge indices from topological insulators to the case of a finite sample with open boundary conditions, and provide a physical interpretation of these…
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.
We study bulk-boundary correspondences and related surface phenomena stabilized by the second Chern number in three-dimensional insulators driven in adiabatic cycles. Magnetic fields and disorder effects are incorporated in our analysis…