Momentum-dependent mass and AC Hall conductivity of quantum anomalous Hall insulators and their relation to the parity anomaly

Abstract

The Dirac mass of a two-dimensional QAH insulator is directly related to the parity anomaly of planar quantum electrodynamics, as shown initially by Niemi and Semenoff [Phys. Rev. Lett. 51, 2077 (1983)PRLTAO0031-900710.1103/PhysRevLett.51.2077]. In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. We reveal that in the calculation of the effective action, before renormalization, the Newtonian mass acts similar to a parity-breaking element of a high-energy regularization scheme. This calculation allows us to derive the finite frequency correction to the DC Hall conductivity of a QAH insulator. We predict that the leading order AC correction contains a term proportional to the Chern number. This term originates from the Newtonian mass and can be measured via electrical or magneto-optical experiments. Moreover, we prove that the Newtonian mass significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene.