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

Author

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  • Daniel Kaplan

    (Weizmann Institute of Science)

  • Tobias Holder

    (Weizmann Institute of Science)

  • Binghai Yan

    (Weizmann Institute of Science)

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.

Suggested Citation

  • Daniel Kaplan & Tobias Holder & Binghai Yan, 2023. "General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect," Nature Communications, Nature, vol. 14(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:14:y:2023:i:1:d:10.1038_s41467-023-38734-9
    DOI: 10.1038/s41467-023-38734-9
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    References listed on IDEAS

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    1. Tingxin Li & Shengwei Jiang & Bowen Shen & Yang Zhang & Lizhong Li & Zui Tao & Trithep Devakul & Kenji Watanabe & Takashi Taniguchi & Liang Fu & Jie Shan & Kin Fai Mak, 2021. "Quantum anomalous Hall effect from intertwined moiré bands," Nature, Nature, vol. 600(7890), pages 641-646, December.
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    3. Yang Zhang & Tobias Holder & Hiroaki Ishizuka & Fernando Juan & Naoto Nagaosa & Claudia Felser & Binghai Yan, 2019. "Switchable magnetic bulk photovoltaic effect in the two-dimensional magnet CrI3," Nature Communications, Nature, vol. 10(1), pages 1-7, December.
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    5. U. Zondiner & A. Rozen & D. Rodan-Legrain & Y. Cao & R. Queiroz & T. Taniguchi & K. Watanabe & Y. Oreg & F. Oppen & Ady Stern & E. Berg & P. Jarillo-Herrero & S. Ilani, 2020. "Cascade of phase transitions and Dirac revivals in magic-angle graphene," Nature, Nature, vol. 582(7811), pages 203-208, June.
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    Cited by:

    1. Ilia Komissarov & Tobias Holder & Raquel Queiroz, 2024. "The quantum geometric origin of capacitance in insulators," Nature Communications, Nature, vol. 15(1), pages 1-8, December.

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