Related papers: The Bulk-Edge Correspondence for Disordered Chiral…

We construct a model of a three-dimensional chiral second-order topological insulator (SOTI) from an array of weakly coupled nanowires. We show that, in a suitable parameter regime, the interplay between rotating magnetic fields and…

Topological crystalline insulators (TCIs) are classified by topological invariants defined with respect to the crystalline symmetries of their gapped bulk. The bulk-boundary correspondence then links the topological properties of the bulk…

We derive a scheme for systematically enumerating the responses of gapped as well as gapless systems of free fermions to electromagnetic and strain fields starting from a common parent theory. Using the fact that position operators in the…

We present the exhaustive classification of surface states of topological insulators and superconductors protected by crystallographic magnetic point group symmetry in three spatial dimensions. Recently, Cornfeld and Chapman [Phys. Rev. B…

We consider the topological protection of entanglement and particle fluctuations for a general one-dimensional chiral topological insulator with winding number $\mathcal{I}$. We prove, in particular, that when the periodic system is divided…

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…

We give field theory descriptions of the time-reversal invariant quantum spin Hall insulator in 2+1 dimensions and the particle-hole symmetric insulator in 1+1 dimensions in terms of massive Dirac fermions. Integrating out the massive…

For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…

We investigate the realization of chiral symmetry in the vicinity of the deconfinement transition in quenched QCD using overlap fermions. Via the index theorem obeyed by the overlap fermions, we gain insight into the behavior of topology at…

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…

This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.

We study symmetry breaking quantum phase transitions in topological insulators and superconductors where the single electron gap remains open in the bulk. Specifically, we consider spontaneous breaking of the symmetry that protects the…

We show here that numerous examples abound where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard non-interacting picture. From extensive determinantal and dynamical cluster quantum…

The scaling behavior of the quantum phase transition from an insulator to a quantum Hall plateau state has often been examined within systems realizing Landau levels. We study the topological transition in energy band models with nonzero…

Chiral symmetry plays an indispensable role in topological classifications as well as in the understanding of the origin of bulk or boundary flat bands. The conventional definition of chiral symmetry refers to the existence of a constant…

We present a distinct mechanism for the formation of bound states in the continuum (BICs). In chiral quantum systems there appear zero-energy states in which the wave function has finite amplitude only in one of the subsystems defined by…

We define an index for invertible phases of two-dimensional fermionic and bosonic quantum spin systems without any additional symmetry. Conjecturally, it provides a microscopic definition of an invariant related to the chiral central charge…

Topological insulators represent a new state of matter where the topological nature of the bulk bands dictates the existence of a surface state with unique properties. These materials are predicted to host exotic states such as Majorana…

The existence of an excitation gap in the bulk spectrum is one of the most prominent fingerprints of topological phases of matter. In this paper, we propose a family of two dimensional Hamiltonians that yield an unusual class $D$…

One of the most intriguing and fundamental properties of topological materials is the correspondence between the conducting edge states and the gapped bulk spectrum. So far, it has been impossible to access the full evolution of edge states…