Generalized bulk-edge correspondence for non-hermitian topological systems

TL;DR

This paper introduces a modified boundary condition for non-hermitian topological systems, enabling a generalized bulk-edge correspondence by defining a topological number similar to hermitian systems, and demonstrates this with a non-hermitian SSH model.

Contribution

It proposes a new boundary condition and topological number for non-hermitian systems, extending the bulk-edge correspondence concept to these systems.

Findings

Defined a topological number for non-hermitian systems

Proved bulk-edge correspondence in a generalized parameter space

Identified a topologically nontrivial region with protected edge states

Abstract

A modified periodic boundary condition adequate for non-hermitian topological systems is proposed. Under this boundary condition a topological number characterizing the system is defined in the same way as in the corresponding hermitian system and hence, at the cost of introducing an additional parameter that characterizes the non-hermitian skin effect, the idea of bulk-edge correspondence in the hermitian limit can be applied almost as it is. We develop this framework through the analysis of a non-hermitian SSH model with chiral symmetry, and prove the bulk-edge correspondence in a generalized parameter space. A finite region in this parameter space with a nontrivial pair of chiral winding numbers is identified as topologically nontrivial, indicating the existence of a topologically protected edge state under open boundary.