Non-Hermitian band topology with generalized inversion symmetry

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 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.

Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

“…Note added-While preparing this manuscript, we became aware of a recent related work [55], which also investigates non-Hermitian symmetry indicators, but focuses on bulk exceptional points and lines in 2D and 3D.…”