# Magnetoresistance in Noncentrosymmetric Two-dimensional Systems

## TL;DR

This paper investigates weak-field magnetoresistance in two-dimensional multi-valley systems with broken inversion symmetry, providing exact solutions to the Boltzmann equation and revealing how in-scattering terms influence magnetoresistance sign and valley polarization effects.

## Contribution

It offers an exact solution to the Boltzmann equation for 2D multi-valley systems, highlighting the impact of in-scattering on magnetoresistance and introducing a valley-polarization probe.

## Key findings

- In-scattering terms can reverse magnetoresistance sign at high density.
- Valley polarization affects magnetoresistance behavior.
- Intrinsic orbital magnetic moment contributes to Hall conductivity.

## Abstract

The valley-contrasting geometric features of electronic wave functions manifested in Berry curvature and orbital magnetic moment have profound consequences on magnetotransport properties in both three- and two-dimensional systems. Although the importance of employing beyond-relaxation-time-approximation methods and intervalley scatterings in collision integral has been confirmed in three dimensions, they have been widely overlooked in previous studies on two-dimensional multi-valley systems. Here, we revisit the issue of weak-field magnetoresistance in two-dimensional multi-valley systems with broken inversion symmetry. We provide an exact solution to the Boltzmann equation and demonstrate that the inclusion of in-scattering terms in the collision integral can change the sign of the magnetoresistance in high-density regime. With an initial valley polarization, we also predict an orbital magnetic moment-induced intrinsic contribution to Hall conductivity in the time-reversal-broken situation, which is consistently negative, and in contrast to the anomalous Hall term, it does not depend on the polarization sign. Depending on which valley has the excess charge, our calculations show that a completely various behavior is exhibited in the magnetoresistance which can be considered as a valley-polarization probe in the experiment.