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

Daniel Kaplan, Tobias Holder and Binghai Yan ()
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Daniel Kaplan: Weizmann Institute of Science
Tobias Holder: Weizmann Institute of Science
Binghai Yan: Weizmann Institute of Science

Nature Communications, 2023, vol. 14, issue 1, 1-7

Abstract: 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 while 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, which can be identified as a new type of multiferroic coupling. 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.

Date: 2023
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DOI: 10.1038/s41467-023-38734-9

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