An upper and lower bound to the orientation-dependent linear Rashba spin-orbit coupling of two-dimensional hole gases in semiconductor quantum wells

TL;DR

This paper investigates how the orientation of semiconductor quantum wells affects the linear Rashba spin-orbit coupling in two-dimensional hole gases, revealing bounds and orientation-specific behaviors through atomistic calculations.

Contribution

It uncovers upper and lower bounds for orientation-dependent Rashba SOC and identifies the exclusive presence of k-cubic Rashba SOC in [111]-oriented quantum wells.

Findings

Maximal HH-LH mixing in [110]-oriented QWs

Only k-cubic Rashba SOC in [111]-oriented QWs

Provides predictions for experimental realization of large Rashba SOC

Abstract

Our recent study [Phys. Rev. B 103, 085309 (2021)] verified the existence of $\bf{k}$-linear Rashba spin-orbit coupling (SOC) of two-dimensional hole gases in quantum wells (QWs) which originates from a combination of heavy-hole-light-hole (HH-LH) mixing and direct dipolar coupling to the external electric field. However, the Rashba SOC dependence on QW orientations remains unclear. Here, we explore this dependence on QW orientations and uncover an upper and lower bound to the orientation-dependent $\bf{k}$-linear Rashba SOC along the [110]- and [111]- crystalline directions by performing atomistic pseudopotential calculations associated with theoretical analysis. The intrinsic HH-LH mixing at the Brillouin zone center, maximal in [110]-oriented quantum wells and minimal in [111]- and [001]-oriented QWs, plays an essential role. Remarkably, we find that only $\bf{k}$-cubic Rashba SOC exists in [111]-oriented QWs. These findings help understand the physical mechanism of the Rashba SOC dependence on QW orientations and provide a strategic prediction for experiments to realize the large Rashba SOC.