Anisotropic modification of the effective hole $g$-factor by electrostatic confinement

TL;DR

This study explores how lateral confinement influences spin splitting and the effective hole g-factor in 2D hole gases on GaAs, revealing anisotropic effects and unexpected dependencies on confinement direction and energy levels.

Contribution

It demonstrates the anisotropic modification of the effective hole g-factor due to electrostatic confinement and uncovers directional and energy level dependencies in spin splitting behavior.

Findings

Lateral confinement enhances anisotropy of spin splitting.

The effective g-factor is independent of energy level number N for B||[0-1 1].

Non-quantized spin-split plateaus occur only in the [0-1 1] confinement direction.

Abstract

We investigate effects of lateral confinement on spin splitting of energy levels in 2D hole gases grown on [311] GaAs. We found that lateral confinement enhances anisotropy of spin splitting relative to the 2D gas for both confining directions. Unexpectedly, the effective $g$-factor does not depend on the 1D energy level number $N$ for $B\|[0\bar{1}1]$ while it has strong $N$-dependence for $B\|[\bar{2}33]$. Apart from quantitative difference in the spin splitting of energy levels for the two orthogonal confinement directions we also report qualitative differences in the appearance of spin-split plateaus, with non-quantized plateaus observed only for the confinement in $[0\bar{1}1]$ direction. In our samples we can clearly associate the difference with anisotropy of spin-orbit interactions.