The Bulk-Edge Correspondence in Three Simple Cases

TL;DR

This paper illustrates the bulk-edge correspondence in simple topological insulator models across three symmetry classes, providing clear examples and a new formula for the b2-index in time-reversal invariant systems.

Contribution

It offers straightforward examples of bulk-edge correspondence in simple models and introduces a new b2-index formula for time-reversal invariant topological insulators.

Findings

Simplified proofs of bulk-edge correspondence in three symmetry classes.

New b2-index formula for time-reversal invariant systems.

Clarifies the mechanism behind bulk-edge principle.

Abstract

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 without the overhead of the more general proofs which are available. We also give a new formula for the \mathbb{Z}_{2}-index of our time-reversal invariant systems inspired by Moore and Balents.