Temperature and Chemical Potential Dependence of the Parity Anomaly in Quantum Anomalous Hall Insulators

TL;DR

This paper investigates how temperature and chemical potential influence the parity anomaly and Hall conductivity in 2D quantum anomalous Hall insulators, revealing that the anomaly remains unrenormalized by temperature but affects topological and thermal responses.

Contribution

It provides a detailed analysis of the temperature and chemical potential dependence of the parity anomaly in quantum anomalous Hall insulators, including the effects of magnetic fields and relativistic versus non-relativistic masses.

Findings

Parity anomaly is not renormalized by finite temperature.

Two terms in Hall conductivity relate to topological and thermal responses.

Relativistic mass counteracts temperature effects, non-relativistic mass enhances them.

Abstract

The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a momentum-dependent mass term. Each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. In this work, we analyze the finite temperature Hall conductivity of a single Chern insulator in 2+1 space-time dimensions under the influence of a chemical potential and an out-of-plane magnetic field. At zero magnetic field, this non-dissipative transport coefficient originates from the parity anomaly of planar quantum electrodynamics. We show that the parity anomaly itself is not renormalized by finite temperature effects. However, it induces two terms of different physical origin in the effective action of a Chern insulator, which is proportional to the Hall conductivity. The first term is temperature and chemical potential independent, and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction and valence band states. In particular, we show that the relativistic mass of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic mass enhances these corrections. Moreover, we extend our analysis to finite magnetic fields and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in orbital fields.