# Interplay of Lorentz-Berry forces in position-momentum spaces for valley-dependent impurity scattering in alpha-T3 lattices

## TL;DR

This paper investigates how Lorentz and Berry forces influence valley-dependent impurity scattering in alpha-T3 lattices, revealing complex interactions affecting electronic transport and Hall effects.

## Contribution

It introduces a detailed analysis of Lorentz-Berry force interplay and includes many-body screening effects, providing new insights into valley-dependent scattering and transport phenomena.

## Key findings

- Triplet peak in skew interactions at two valleys for small Berry phases.
- Magnetic-field dependence of valley-dependent currents analyzed.
- Valley-dependent anomalous Hall current computed considering Berry force.

## Abstract

The Berry-phase mediated valley-selected skew scattering in alpha-T3 lattices is demonstrated. The interplay of Lorentz and Berry forces in position and momentum spaces is revealed and analyzed. Many-body screening of the electron-impurity interaction is taken into account to avoid overestimation of back- and skew-scattering of electrons in the system. Triplet peak from skew interactions at two valleys is found in near-vertical and near-horizontal forward- and backward-scattering directions for small Berry phases and low magnetic fields. Magnetic-field dependence in both non-equilibrium and thermal-equilibrium currents is also presented for valley-dependent longitudinal and transverse transports mediated by a Berry phase. Mathematically, two Boltzmann moment equations are employed for computing scattering-angle distributions of non-equilibrium skew currents by using microscopic inverse energy- and momentum-relaxation times. Meanwhile, a valley-dependent unbalanced thermal-equilibrium anomalous Hall current induced by the Berry force in momentum space, due to different mobilities for two valleys, is also computed for comparisons.