# Inversion symmetric non-Hermitian Chern insulator

## TL;DR

This paper introduces a non-Hermitian Chern insulator with inversion symmetry, demonstrating how topological invariants predict edge states and phase transitions, including in gapless and zero Chern number phases, with implications for symmetry-protected topological insulators.

## Contribution

It presents a novel model of a non-Hermitian Chern insulator with inversion symmetry, analyzing its topological phases, edge states, and the role of exceptional points and winding numbers.

## Key findings

- Bulk-boundary correspondence holds in this system.
- Helical edge states exist in the gapless phase under certain conditions.
- Zero Chern number phase can host in-gap edge states.

## Abstract

We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial gapped phase. In the gapless phase, the band touching points are isolated and protected by the symmetry. The degenerate points alter the system topology, and the exceptional points can destroy the existence of helical edge states. Topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction, which are predicted by the winding number associated with the vector field of average values of Pauli matrices. The winding number also identifies the detaching points between the edge states and the bulk states in the energy bands. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.