Microlocal analysis of the bulk-edge correspondence

TL;DR

This paper proves the bulk-edge correspondence for PDEs using semiclassical methods, providing new insights into topologically protected transport at interfaces of topological insulators.

Contribution

It introduces a novel proof of the bulk-edge correspondence for PDEs with periodic structures using semiclassical analysis.

Findings

Validated the bulk-edge correspondence for a class of PDEs

Provided a new semiclassical framework for topological transport analysis

Suggested potential for broader applications in topological materials

Abstract

The bulk-edge correspondence predicts that interfaces between topological insulators support robust currents. We prove this principle for PDEs that are periodic away from an interface. Our approach relies on semiclassical methods. It suggests novel perspectives for the analysis of topologically protected transport.