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

## TL;DR

This paper develops a modified semiclassical Boltzmann framework incorporating interband coherence effects to better understand nonlinear Hall effects, validated through quantum kinetic theory in tilted Dirac models.

## Contribution

It introduces a new semiclassical approach that accounts for interband coherence effects in nonlinear transport, extending traditional Boltzmann theory.

## Key findings

- New contribution from interband coherence during scattering
- Validated semiclassical approach with quantum kinetic theory
- Demonstrated in nonlinear Hall effect of tilted Dirac model

## 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.