Spin-orbit interactions in inversion-asymmetric 2D hole systems: a variational analysis

TL;DR

This paper develops a semi-analytical variational method to analyze spin-orbit interactions in inversion-asymmetric 2D hole systems across various semiconductors, revealing limitations of the simple Rashba model and providing accurate parameter calculations.

Contribution

The paper introduces a new semi-analytical approach to quantify spin-orbit interactions in 2D hole gases, highlighting the breakdown of the simple Rashba model and offering improved parameter estimation methods.

Findings

The simple SW approximation often fails to accurately describe spin splitting.

BIA terms are significantly smaller than SIA terms in studied heterostructures.

The method aligns well with numerical calculations and experimental data.

Abstract

We present an in-depth study of the spin-orbit (SO) interactions occurring in inversion-asymmetric two-dimensional hole gases at semiconductor heterointerfaces. We focus on common semiconductors such as GaAs, InAs, InSb, Ge, and Si. We develop a semi-analytical variational method to quantify SO interactions, accounting for both structure inversion asymmetry (SIA) and bulk inversion asymmetry (BIA). Under certain circumstances, using the Schrieffer-Wolff (SW) transformation, the dispersion of the ground state heavy hole subbands can be written as $E(k) = A k^2 - B k^4 \pm C k^3$ where $A$, $B$, and $C$ are material- and structure-dependent coefficients. We provide a simple method of calculating the parameters $A$, $B$, and $C$, yet demonstrate that the simple SW approximation leading to a SIA (Rashba) spin splitting $\propto k^3$ frequently breaks down. We determine the parameter regimes at which this happens for the materials above and discuss a convenient semi-analytical method to obtain the correct spin splitting, effective masses, Fermi level, and subband occupancy, together with their dependence on the charge density, dopant type, and dopant concentration for both inversion and accumulation layers. Our results are in good agreement with fully numerical calculations as well as with experimental findings. They suggest that a naive application of the simple cubic Rashba model is of limited use in common heterostructures, as well as quantum dots. Finally, we find that for the single heterojunctions studied here the magnitudes of BIA terms are always much smaller than those of SIA terms.