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The Dirac mass of a two-dimensional QAH insulator is directly related to theparity anomaly of planar quantum electrodynamics, as shown initially in Phys.Rev. Lett. 52, 18 (1984). In this work, we connect the additionalmomentum-dependent Newtonian mass term of a QAH insulator to the parityanomaly. By calculating the effective action, we reveal that the Newtonian massterm acts like a parity-breaking element of a high-energy regularizationscheme. As such, it is directly related to the parity anomaly. In addition, thecalculation of the effective action allows us to determine the finite frequencycorrection to the DC Hall conductivity of a QAH insulator. We derive that theleading order AC correction contains a term proportional to the torsional Hallviscosity. This paves the way to measure this non-dissipative transportcoefficient via electrical or magneto-optical experiments. Moreover, we provethat the Newtonian mass significantly changes the resonance structure of the ACHall conductivity in comparison to pure Dirac systems like graphene.

Momentum-Dependent Mass and AC Hall Conductivity of Quantum Anomalous Hall Insulators and Their Relation to the Parity Anomaly