Edge states in a non-Hermitian topological crystalline insulator

TL;DR

This paper investigates non-Hermitian topological crystalline insulators on a Kekulé-modulated honeycomb lattice, revealing that edge state gaplessness remains robust under moderate gain and loss, with distinct effects for PT-symmetric and PT-asymmetric configurations.

Contribution

It demonstrates the insensitivity of topological edge state gaplessness to edge geometries in non-Hermitian systems and explores the effects of PT-symmetric and PT-asymmetric gain and loss configurations.

Findings

Edge state gaplessness is robust against edge geometry under moderate gain/loss.

PT-symmetric gain/loss causes Dirac points to split into exceptional points.

Edge and bulk band gaps close simultaneously in PT-asymmetric configurations.

Abstract

Breaking Hermiticity in topological systems gives rise to intriguing phenomena, such as the exceptional topology and the non-Hermitian skin effect. In this work, we study a non-Hermitian topological crystalline insulator sitting on the Kekul\'{e}-modulated honeycomb lattice with balanced gain and loss. We find that the gaplessness of the topological edge states in the non-Hermitian system is insensitive to edge geometries under moderate strength of gain and loss, unlike the cases of Hermitian topological crystalline insulators that depend on edge geometries crucially. We focus on two types of gain and loss configurations, which are $PT$-symmetric and $PT$-asymmetric, respectively. For the $PT$-symmetric configuration, the Dirac point of the topological edge states in the Hermitian molecular-zigzag-terminated ribbons splits into a pair of exceptional points. The edge gap in the Hermitian armchair-terminated ribbons vanishes and a Dirac point forms as far as moderate gain and loss is induced. The band gaps of edge and bulk states in the Hermitian armchair-terminated ribbons close simultaneously for the $PT$-asymmetric configuration.