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Quantum theory of the nonlinear Hall effect

Author

Listed:
  • Z. Z. Du

    (Southern University of Science and Technology (SUSTech)
    Shenzhen Key Laboratory of Quantum Science and Engineering)

  • C. M. Wang

    (Southern University of Science and Technology (SUSTech)
    Shenzhen Key Laboratory of Quantum Science and Engineering
    Shanghai Normal University)

  • Hai-Peng Sun

    (Southern University of Science and Technology (SUSTech)
    Shenzhen Key Laboratory of Quantum Science and Engineering)

  • Hai-Zhou Lu

    (Southern University of Science and Technology (SUSTech)
    Shenzhen Key Laboratory of Quantum Science and Engineering)

  • X. C. Xie

    (School of Physics, Peking University
    University of Chinese Academy of Sciences
    Beijing Academy of Quantum Information Sciences)

Abstract

The nonlinear Hall effect is an unconventional response, in which a voltage can be driven by two perpendicular currents in the Hall-bar measurement. Unprecedented in the family of the Hall effects, it can survive time-reversal symmetry but is sensitive to the breaking of discrete and crystal symmetries. It is a quantum transport phenomenon that has deep connection with the Berry curvature. However, a full quantum description is still absent. Here we construct a quantum theory of the nonlinear Hall effect by using the diagrammatic technique. Quite different from nonlinear optics, nearly all the diagrams account for the disorder effects, which play decisive role in the electronic transport. After including the disorder contributions in terms of the Feynman diagrams, the total nonlinear Hall conductivity is enhanced but its sign remains unchanged for the 2D tilted Dirac model, compared to the one with only the Berry curvature contribution. We discuss the symmetry of the nonlinear conductivity tensor and predict a pure disorder-induced nonlinear Hall effect for point groups C3, C3h, C3v, D3h, D3 in 2D, and T, Td, C3h, D3h in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.

Suggested Citation

  • Z. Z. Du & C. M. Wang & Hai-Peng Sun & Hai-Zhou Lu & X. C. Xie, 2021. "Quantum theory of the nonlinear Hall effect," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-25273-4
    DOI: 10.1038/s41467-021-25273-4
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    Cited by:

    1. Xiu Fang Lu & Cheng-Ping Zhang & Naizhou Wang & Dan Zhao & Xin Zhou & Weibo Gao & Xian Hui Chen & K. T. Law & Kian Ping Loh, 2024. "Nonlinear transport and radio frequency rectification in BiTeBr at room temperature," Nature Communications, Nature, vol. 15(1), pages 1-9, December.
    2. Yudi Dai & Junlin Xiong & Yanfeng Ge & Bin Cheng & Lizheng Wang & Pengfei Wang & Zenglin Liu & Shengnan Yan & Cuiwei Zhang & Xianghan Xu & Youguo Shi & Sang-Wook Cheong & Cong Xiao & Shengyuan A. Yang, 2024. "Interfacial magnetic spin Hall effect in van der Waals Fe3GeTe2/MoTe2 heterostructure," Nature Communications, Nature, vol. 15(1), pages 1-10, December.
    3. Lujin Min & Hengxin Tan & Zhijian Xie & Leixin Miao & Ruoxi Zhang & Seng Huat Lee & Venkatraman Gopalan & Chao-Xing Liu & Nasim Alem & Binghai Yan & Zhiqiang Mao, 2023. "Strong room-temperature bulk nonlinear Hall effect in a spin-valley locked Dirac material," Nature Communications, Nature, vol. 14(1), pages 1-9, December.

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