Pseudo-Hermitian Topology of Multiband Non-Hermitian Systems

TL;DR

This paper explores the topological properties of multiband non-Hermitian systems, highlighting the role of pseudo-Hermitian lines and demonstrating that non-trivial topology can exist without exceptional points, with applications in photonic crystals.

Contribution

It introduces the concept of pseudo-Hermitian lines in non-Hermitian topology and shows non-separable multiband systems can be topologically non-trivial without exceptional points.

Findings

Non-separable multiband systems can have non-trivial topology without exceptional points.

Pseudo-Hermitian lines play a crucial role in non-Hermitian topological classification.

Application demonstrated in a photonic crystal with lossy materials.

Abstract

The complex eigenenergies and non-orthogonal eigenstates of non-Hermitian systems exhibit unique topological phenomena that cannot appear in Hermitian systems. Representative examples are the non-Hermitian skin effect and exceptional points. In a two-dimensional parameter space, topological classifications of non-separable bands in multiband non-Hermitian systems can be established by invoking a permutation group, where the product of the permutation represents state exchange due to exceptional points in the space. We unveil in this work the role of pseudo-Hermitian lines in non-Hermitian topology for multiple bands. In particular, the non-separability of non-Hermitian multibands can be topologically non-trivial without exceptional points in two-dimensional space. As a physical illustration of the role of pseudo-Hermitian lines, we examine a multiband structure of a photonic crystal system with lossy materials. Our work builds on the fundamental and comprehensive understanding of non-Hermitian multiband systems and also offers versatile applications and realizations of non-Hermitian systems without the need to consider exceptional points.