# Spin-orbit coupling and transport of strongly correlated two-dimensional systems

## TL;DR

This study investigates how spin-orbit coupling influences magnetoresistance in ultraclean GaAs two-dimensional holes, revealing a sign change at the metal-insulator transition and an enhanced SOC effect near the critical density, highlighting complex interplay between SOC and electron interactions.

## Contribution

It uncovers the relationship between spin-orbit coupling, magnetoresistance sign change, and electron-electron interactions near the metal-insulator transition in 2D systems.

## Key findings

- MR sign switches at the MIT critical density
- Enhanced SOC effects near the critical density
- Negative MR linked to interactions beyond Wigner crystallization

## Abstract

Measuring the magnetoresistance (MR) of ultraclean {\it GaAs} two-dimensional holes in a large $r_s$ range of 20-50, two striking behaviors in relation to the spin-orbit coupling (SOC) emerge in response to strong electron-electron interaction. First, in exact correspondence to the zero-field metal-to-insulator transition (MIT), the sign of the MR switches from being positive in the metallic regime to being negative in the insulating regime when the carrier density crosses the critical density $p_c$ of MIT ($r_s\sim 39$). Second, as the SOC-driven correction $\Delta\rho$ to the MR decreases with reducing carrier density (or the in-plane wave vector), it exhibits an upturn in the close proximity just above $p_c$ where $r_s$ is beyond 30, indicating a substantially enhanced SOC effect. This peculiar behavior echoes with a trend of delocalization long suspected for the SOC-interaction interplay. Meanwhile, for $p<p_c$ or $r_s>40$, in contrast to the common belief that a magnet field enhances Wigner crystallization, the negative MR is likely linked to enhanced interaction.