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Abstract
The nonlinear Hall effect has opened the door towards deeper understanding of topological states of matter. Disorder plays indispensable roles in various linear Hall effects, such as the localization in the quantized Hall effects and the extrinsic mechanisms of the anomalous, spin, and valley Hall effects. Unlike in the linear Hall effects, disorder enters the nonlinear Hall effect even in the leading order. Here, we derive the formulas of the nonlinear Hall conductivity in the presence of disorder scattering. We apply the formulas to calculate the nonlinear Hall response of the tilted 2D Dirac model, which is the symmetry-allowed minimal model for the nonlinear Hall effect and can serve as a building block in realistic band structures. More importantly, we construct the general scaling law of the nonlinear Hall effect, which may help in experiments to distinguish disorder-induced contributions to the nonlinear Hall effect in the future.
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Details
1 Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China; Peng Cheng Laboratory, Shenzhen, China
2 Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China; Department of Physics, Shanghai Normal University, Shanghai, China
3 Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China
4 Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, China; Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China; Peng Cheng Laboratory, Shenzhen, China; Tsung-Dao Lee Institute, Shanghai Jiao Tong University, Shanghai, China
5 International Center for Quantum Materials, School of Physics, Peking University, Beijing, China; Beijing Academy of Quantum Information Sciences, Beijing, China; CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing, China