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

• URL: http://arxiv.org/abs/2101.02393v2
• Date: Fri, 2 Apr 2021 12:39:58 GMT
• Title: Hall conductance of a non-Hermitian two-band system with k-dependent decay rates
• Authors: Junjie Wang, Fude Li, and X. X. Yi
• Abstract summary: We derive an effective non-Hermitian Hamiltonian to describe the system and give a specific form of k-dependent decay rate. We calculate the response of the non-Hermitian system to a constant electric field.
• Score: 2.105031112138881
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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