# Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics

Source: [Theory of nonlinear Hall effects: renewed semiclassics from quantum kinetics](<https://www.sota2.com/research/paper/68fa3ad61e209131ce8cdf20>)

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

Data updated: 2025-10-25T00:17:41.495Z

Authors: Cong Xiao, Z. Z. Du, Qian Niu

Published: 2019-07-01T07:12:11.000Z

## Abstract

We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows from the interband-coherence effect of dc electric-fields during scattering and is related to the interband Berry connection. As an application, we demonstrate it in the second-order nonlinear Hall effect of the tilted massive Dirac model. The intuitive Boltzmann constructions are confirmed by a quantum kinetic theory, which shows that arbitrary $n$th-order nonlinear dc response up to the first three leading contributions in the weak disorder potential is handled by the same few gauge-invariant semiclassical ingredients.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1907.00577>)

[PDF](<https://arxiv.org/pdf/1907.00577.pdf>)