This paper constructs a quantum theory of the nonlinear Hall effect using the diagrammatic technique. Unlike previous semiclassical theories, this work explicitly incorporates disorder effects, which are shown to be crucial for electronic transport. The analysis includes 69 Feynman diagrams representing intrinsic, side-jump, and skew-scattering contributions. Applying the theory to a 2D tilted Dirac model reveals that disorder enhances the nonlinear Hall conductivity while preserving its sign. A symmetry analysis predicts a pure disorder-induced nonlinear Hall effect for specific point groups in 2D and 3D.

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