Hall Conductance of a Non-Hermitian Chern Insulator

TL;DR

This paper investigates how non-Hermitian terms affect the Hall conductance in Chern insulators, revealing deviations from quantization due to bulk broadening and edge decay, and provides a generalized formula for the topological contribution.

Contribution

It introduces a simple formula for the topological Hall conductance in non-Hermitian Chern insulators, extending the TKNN formula to non-Hermitian systems.

Findings

Non-Hermitian terms cause non-universal bulk contributions to Hall conductance.

Decay in edge states leads to deviations from quantized Chern numbers.

The derived formula predicts increased deviation with stronger or more momentum-dependent non-Hermitian terms.

Abstract

In this letter we study the Hall conductance for a non-Hermitian Chern insulator and quantitatively describe how the Hall conductance deviates from a quantized value. We show the effects of the non-Hermitian terms on the Hall conductance are two folds. On one hand, it broadens the density-of-state of each band, because of which there always exists a non-universal bulk contribution. On the other hand, it adds decay term to the edge state, because of which the topological contribution also deviates from the quantized Chern number. We provides a simple formula for the topological contribution for a general two-band non-Hermitian Chern insulator, as a non-Hermitian version of the Thouless-Kohmoto-Nightingale-de Nijs formula. It shows that the derivation from quantized value increases either when the strength of the non-Hermitian term increases, or when the momentum dependence of the non-Hermitian term increases. Our results can be directly verified in synthetic non-Hermitian topological systems where the strength of the non-Hermitian terms can be controlled.