Hall conductance of a non-Hermitian two-band system with k-dependent decay rates

TL;DR

This paper investigates how a non-Hermitian two-band topological insulator responds to an electric field, revealing environment-induced modifications to Hall conductance and its relation to the system's topology.

Contribution

It introduces a model for a non-Hermitian Chern insulator with k-dependent decay rates and analyzes its electric field response, connecting non-Hermitian topology to measurable conductance.

Findings

Hall conductance becomes a weighted integral of curvature, losing quantization

Environment causes a delay in the system's response to electric fields

Derived an effective non-Hermitian Hamiltonian for the system

Abstract

Two-band model works well for Hall effect in topological insulators. It turns out to be non-Hermitian when the system is subjected to environments, and its topology characterized by Chern numbers has received extensive studies in the past decades. However, how a non-Hermitian system responses to an electric field and what is the connection of the response to the Chern number defined via the non-Hermitian Hamiltonian remain barely explored. In this paper, focusing on a k-dependent decay rate, we address this issue by studying the response of such a non-Hermitian Chern insulator to an external electric field. To this aim, we first derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. Then we calculate the response of the non-Hermitian system to a constant electric field. We observe that the environment leads the Hall conductance to be a weighted integration of curvature of the ground band and hence the conductance is no longer quantized in general. And the environment induces a delay in the response of the system to the electric field. A discussion on the validity of the non-Hermitian model compared with the master equation description is also presented.