Bulk-edge correspondence for Chern topological phases: A viewpoint from a generalized index theorem

TL;DR

This paper demonstrates a generalized index theorem approach to establish the bulk-edge correspondence in Chern topological phases, linking edge spectral flow with bulk Chern numbers in complex band structures.

Contribution

It introduces a generalized index theorem framework applicable to systems with higher order derivatives, extending the understanding of bulk-edge correspondence in topological insulators.

Findings

Spectral flow of edge states equals bulk Chern numbers.

Generalized index theorem applies to complex band structures.

Bulk-edge correspondence holds without time-reversal symmetry.

Abstract

We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear dispersion but also with higher order derivatives arising from generic band structures. Using a generalized index theorem valid for such systems, we show the equivalence between the spectral flow of the edge states and the Chern numbers specifying the bulk systems.