Non-Hermitian $C_{NH} = 2$ Chern insulator protected by generalized rotational symmetry

TL;DR

This paper introduces a non-Hermitian topological insulator protected by a generalized rotational symmetry, featuring a non-Hermitian Chern number of 2 and multiple in-gap edge states, advancing the understanding of non-Hermitian topological phases.

Contribution

It proposes a new non-Hermitian topological system with a non-Hermitian Chern number of 2, protected by generalized rotational symmetry, and demonstrates the existence of multiple edge modes.

Findings

Hosts two pairs of in-gap edge modes in the topological phase

Characterized by a non-Hermitian Chern number of 2

Quantization protected by generalized rotational symmetry

Abstract

We propose a non-Hermitian topological system protected by the generalized rotational symmetry which invokes rotation in space and Hermitian conjugation. The system, described by the tight-binding model with nonreciprocal hopping, is found to host two pairs of in-gap edge modes in the gapped topological phase and is characterized by the non-Hermitian (NH) Chern number $C_{NH}=2$. The quantization of the non-Hermitian Chern number is shown to be protected by the generalized rotational symmetry $\^H^{+}=\^U\^H\^U^{+}$ of the system. Our finding paves the way towards novel non-Hermitian topological systems characterized by large values of topological invariants and hosting multiple in-gap edge states, which can be used for topologically resilient multiplexing.