Asymmetric $g$ tensor in low-symmetry two-dimensional hole systems

TL;DR

This paper investigates the highly anisotropic and asymmetric g tensor in low-symmetry two-dimensional hole systems in GaAs/AlAs quantum wells, combining experimental Kerr rotation measurements with detailed multiband theoretical modeling.

Contribution

It provides the first comprehensive experimental and theoretical analysis of the asymmetric g tensor in low-symmetry 2D hole systems, revealing its non-symmetric nature and detailed component behavior.

Findings

Identification of a non-diagonal, asymmetric g tensor in 2D hole systems.

Good agreement between experimental measurements and theoretical calculations.

Quantification of tensor components for different crystal orientations.

Abstract

The complex structure of the valence band in many semiconductors leads to multifaceted and unusual properties for spin-3/2 hole systems compared to typical spin-1/2 electron systems. In particular, two-dimensional hole systems show a highly anisotropic Zeeman spin splitting. We have investigated this anisotropy in GaAs/AlAs quantum well structures both experimentally and theoretically. By performing time-resolved Kerr rotation measurements, we found a non-diagonal tensor $g$ that manifests itself in unusual precessional motion as well as distinct dependencies of hole spin dynamics on the direction of the magnetic field $\vec{B}$. We quantify the individual components of the tensor $g$ for [113]-, [111]- and [110]-grown samples. We complement the experiments by a comprehensive theoretical study of Zeeman splitting in in-plane and out-of-plane fields $\vec{B}$. To this end, we develop a detailed multiband theory for the tensor $g$. Using perturbation theory, we derive transparent analytical expressions for the components of the tensor $g$ that we complement with accurate numerical calculations based on our theoretical framework. We obtain very good agreement between experiment and theory. Our study demonstrates that the tensor $g$ is neither symmetric nor antisymmetric. Opposite off-diagonal components can differ in size by up to an order of magnitude.