Asymmetric g Tensor in Low-Symmetry Two-Dimensional Hole Systems

C Gradl,C Schüller,J Holler,D Bougeard,M Kempf,R Winkler,A Hernández-Mínguez,D Schuh,K Biermann,P V Santos,T Korn

doi:10.1103/physrevx.8.021068

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.

Highlights

Spin-dependent phenomena in semiconductor heterostructures have been studied intensively in recent years with the prospect of enabling spintronics and quantum information applications [1,2,3,4,5,6,7]
By performing time-resolved Kerr rotation measurements, we found a nondiagonal 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 B
We derive transparent analytical expressions for the components of the tensor g that we complement with accurate numerical calculations based on our theoretical framework

Summary

Introduction

Spin-dependent phenomena in semiconductor heterostructures have been studied intensively in recent years with the prospect of enabling spintronics and quantum information applications [1,2,3,4,5,6,7]. Many studies have investigated the dynamics of electron systems in direct-gap semiconductors like GaAs. Here, bulk systems as well as nanostructures ranging from quantum wells (QWs) to wires and dots have been covered. While electrons in the conduction band of semiconductors such as GaAs are s-like with an effective spin 1=2, the p-like character of holes in the valence band gives rise to an effective spin 3=2 that offers more complex and novel spin-dependent characteristics.

Methods

Discussion

Conclusion