Bulk-edge correspondence and the cobordism invariance of the index

TL;DR

This paper demonstrates that the fundamental bulk-edge correspondence in certain topological insulators is a consequence of the cobordism invariance of the index, linking topological invariants to physical phenomena.

Contribution

It establishes a direct connection between the bulk-edge correspondence and cobordism invariance of the index for 2D topological insulators, providing a new theoretical insight.

Findings

Bulk-edge correspondence derived from cobordism invariance

Applicable to 2D type A and AII topological insulators

Provides a topological proof of the index invariance

Abstract

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.