Temperature and chemical potential dependence of the parity anomaly in quantum anomalous Hall insulators

Christian Tutschku, Flavio S. Nogueira, Christian Northe, Jeroen Van Den Brink, E. M. Hankiewicz

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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 nondissipative 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 nontopological 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 nonrelativistic 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.

Original languageEnglish
Article number205407
JournalPhysical Review B
Issue number20
StatePublished - 5 Nov 2020
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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