Non-Hermitian CNH=2 Chern insulator 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 reciprocal imaginary next-nearest-neighbor 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 ${C}_{\mathrm{NH}}=2$. The quantization of the NH Chern number is shown to be protected by the generalized rotational symmetry ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}^{+}(\mathrm{g}\stackrel{P\vec}{k})={\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{U}}_{g}\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}(\stackrel{P\vec}{k}){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{U}}_{g}^{+}$ of the system. Our finding paves the way towards 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.