Non-Hermitian band topology with generalized inversion symmetry

TL;DR

This paper introduces a method to detect non-Hermitian skin effects and exceptional points using a generalized inversion symmetry, providing simple formulas to analyze topological phenomena in non-Hermitian systems.

Contribution

It develops a novel approach to identify topological features in non-Hermitian systems through generalized inversion symmetry, which is unique to these systems.

Findings

Parity of winding numbers can be determined from energy eigenvalues.

Methods are demonstrated on lattice models for skin effects and exceptional points.

Simple expressions facilitate analysis of non-Hermitian topological phenomena.

Abstract

Non-Hermitian skin effects and exceptional points are topological phenomena characterized by integer winding numbers. In this study, we give methods to theoretically detect skin effects and exceptional points by generalizing inversion symmetry. The generalization of inversion symmetry is unique to non-Hermitian systems. We show that parities of the winding numbers can be determined from energy eigenvalues on the inversion-invariant momenta when generalized inversion symmetry is present. The simple expressions for the winding numbers allow us to easily analyze skin effects and exceptional points in non-Hermitian bands. We also demonstrate the methods for (second-order) skin effects and exceptional points by using lattice models.