General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Abstract

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity and other insulators (with zero Chern number) present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the Integer quantum Hall effect.

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• Equivalence of semiclassical and response theories for second-order nonlinear ac Hall effects
• Quantum kinetic theory of quadratic responses
• Planar Hall Plateau in Magnetic Weyl Semimetals
• Extrinsic Mechanisms of Phonon Magnetic Moment
• Electrical control of intrinsic nonlinear Hall effect in antiferromagnetic topological insulator sandwiches
• Quantum Nonlinear Acoustic Hall Effect and Inverse Acoustic Faraday Effect in Dirac Insulators
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• Quantum theory of nonlinear electromagnetic response
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