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 in Phys. Rev. Lett. 52, 18 (1984). In this work, we connect the additional momentum-dependent Newtonian mass term of a QAH insulator to the parity anomaly. By calculating the effective action, we reveal that the Newtonian mass term acts like a parity-breaking element of a high-energy regularization scheme. As such, it is directly related to the parity anomaly. In addition, the calculation of the effective action allows us to determine the finite frequency correction to the DC Hall conductivity of a QAH insulator. We derive that the leading order AC correction contains a term proportional to the torsional Hall viscosity. This paves the way to measure this non-dissipative transport coefficient 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.

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• Hall viscosity and hydrodynamic inverse Nernst effect in graphene
• Quantum Hall effective action for anisotropic Dirac semi-metal
• Raman tensor for two-dimensional massive Dirac fermions
• Parity anomaly with impurities and the Pauli--Villars subtraction
• Dissipative Callan-Harvey mechanism in 2+1 D Dirac system: The fate of edge states along a domain wall
• Torsional Hall Viscosity of Massive Chern Insulators: Magnetic Field and Momentum Deformations