Quantum theory of the nonlinear Hall effect

Z Z Du; C M Wang; Hai-Peng Sun; Hai-Zhou Lu; X C Xie

doi:10.1038/s41467-021-25273-4

Quantum theory of the nonlinear Hall effect

Nat Commun. 2021 Aug 19;12(1):5038. doi: 10.1038/s41467-021-25273-4.

Authors

Z Z Du^{1

2}, C M Wang^{1

2

3}, Hai-Peng Sun^{1

2}, Hai-Zhou Lu^{4

5}, X C Xie^{6

7

8}

Affiliations

¹ Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China.
² Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China.
³ Department of Physics, Shanghai Normal University, Shanghai, China.
⁴ Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China. luhz@sustech.edu.cn.
⁵ Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China. luhz@sustech.edu.cn.
⁶ International Center for Quantum Materials, School of Physics, Peking University, Beijing, China.
⁷ CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China.
⁸ Beijing Academy of Quantum Information Sciences, Beijing, China.

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, C_3h, C_3v, D_3h, D₃ in 2D, and T, T_d, C_3h, D_3h in 3D. This work will be helpful for explorations of the topological physics beyond the linear regime.