Bulk-edge correspondence for two-dimensional topological insulators

TL;DR

This paper proves the equivalence between bulk and edge descriptions of two-dimensional topological insulators, introduces a new formulation of the $\

Contribution

It provides a novel bulk index formulation for 2D topological insulators that does not depend on the Brillouin zone, extending to quantum Hall systems.

Findings

Bulk-edge correspondence is established for 2D topological insulators.

A new $\

paper_type

Abstract

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 $\mathbb{Z}_{2}$-invariant, which allows for a bulk index not relying on a (two-dimensional) Brillouin zone. When available though, that index is shown to agree with known formulations. The method also applies to integer quantum Hall systems. We discuss a further variant of the correspondence, based on scattering theory.