Non-Bloch band theory and bulk-edge correspondence in non-Hermitian systems

TL;DR

This paper reviews a non-Bloch band theory for one-dimensional non-Hermitian systems, establishing a bulk-edge correspondence by redefining the Brillouin zone to accurately predict edge states.

Contribution

It introduces a non-Bloch band theory that correctly predicts topological edge states in non-Hermitian systems, extending traditional bulk-edge correspondence.

Findings

Redefines the Brillouin zone for non-Hermitian systems

Establishes bulk-edge correspondence using non-Bloch topological invariants

Validates theory with the non-Hermitian Su-Schrieffer-Heeger model

Abstract

In this paper, we review our non-Bloch band theory in one-dimensional non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su-Schrieffer-Heeger model, the bulk-edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.