# Symmetry and Quantum Kinetics of the Non-linear Hall Effect

Source: [Symmetry and Quantum Kinetics of the Non-linear Hall Effect](<https://www.sota2.com/research/paper/68fa3b0b1e209131ce8cf910>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T00:23:50.854Z

Authors: Snehasish Nandy, Inti Sodemann

Published: 2019-01-14T18:59:51.000Z

## Abstract

We argue that the static non-linear Hall conductivity can always be represented as a vector in two-dimensions and as a pseudo-tensor in three-dimensions independent of its microscopic origin. In a single band model with a constant relaxation rate this vector or tensor is proportional to the Berry curvature dipole \\cite{Sodemann\_2015}. Here, we develop a quantum Boltzmann formalism to second order in electric fields. We find that in addition to the Berry Curvature Dipole term, there exist additional disorder mediated corrections to the non-linear Hall tensor that have the same scaling in impurity scattering rate. These can be thought of as the non-linear counterparts to the side-jump and skew-scattering corrections to the Hall conductivity in the linear regime. We illustrate our formalism by computing the different contributions to the non-linear Hall conductivity of two-dimensional tilted Dirac fermions.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1901.04467>)

[PDF](<https://arxiv.org/pdf/1901.04467.pdf>)