# Theory of phonon side jump contribution in Anomalous Hall transport

## TL;DR

This paper develops a Boltzmann theory for phonon side-jump contributions to the anomalous Hall effect, revealing temperature-dependent behavior and enabling quantitative comparisons with experiments.

## Contribution

It introduces a microscopic quantum mechanical derivation of phonon side-jump conductivity within a Boltzmann framework, applicable to ab initio calculations.

## Key findings

- Phonon side-jump conductivity varies with temperature, approaching different limits at high and low temperatures.
- The theory predicts strong temperature dependence in the intermediate regime.
- It provides a foundation for quantitative comparison between theory and experimental measurements.

## Abstract

The role of electron-phonon scattering in finite-temperature anomalous Hall effect is still poorly understood. In this work, we present a Boltzmann theory for the side-jump contribution from electron-phonon scattering, which is derived from the microscopic quantum mechanical theory. We show that the resulting phonon side-jump conductivity generally approaches different limiting values in the high and low temperature limits, and hence can exhibit strong temperature dependence in the intermediate temperature regime. Our theory is amenable to ab initio treatment, which makes quantitative comparison between theoretical and experimental results possible.