Edge modes in band topological insulators

TL;DR

This paper characterizes gapless edge modes in topological insulators, linking their spectrum to topological properties of the occupied state bundle, and illustrates the concepts with Chern insulators and quantum spin Hall states.

Contribution

It introduces a method to relate edge mode spectra to the topology of the occupied state bundle via a gluing function, providing a unified framework for different topological phases.

Findings

Edge modes correspond to non-trivial gluing functions with spectral flow.

The spectrum of edge modes is a continuous deformation of the gluing function spectrum.

Illustrations include chiral edge states in Chern insulators and helical edges in quantum spin Hall states.

Abstract

We characterize gapless edge modes in translation invariant topological insulators. We show that the edge mode spectrum is a continuous deformation of the spectrum of a certain gluing function defining the occupied state bundle over the Brillouin zone (BZ). Topologically non-trivial gluing functions, corresponding to non-trivial bundles, then yield edge modes exhibiting spectral flow. We illustrate our results for the case of chiral edge states in two dimensional Chern insulators, as well as helical edges in quantum spin Hall states.