Spin-orbit interactions in inversion-asymmetric two-dimensional hole systems: A variational analysis

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 aswhere 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 ∝ 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, and dopant type, 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 either common heterostructures or 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.

Spin blockade in hole quantum dots: Tuning exchange electrically and probing Zeeman interactions

“…Theoretical treatments often take this HH-LH splitting to be the largest energy scale (> 10 meV in GaAs inversion layers), whereupon the lowest energy (HH) subband may be described by a pseudospin degree of freedom. While such perturbative treatments may break down in certain parameter regimes [40], they enable direct comparisons between low-dimensional hole and electron systems, and we adopt this picture here. Accordingly, the pseudospin Zeeman interaction has a complex form [41].…”

“…If B points along the tunneling field The values of t0, and tR based on the results α of 2D accumulation (A) and inversion (I) holes [40]. For 2D Si, there is a significant anisotropic Rashba contribution in k , and for hole densities ∼ 10 16 m −2 , the ratio of the Rashba spin splitting to the Fermi energy is roughly 0.1, hence tR ∼ t0/10.…”

“…40 indicates that the perturbative approach will break down if the 2D hole density reaches a critical value. The current model then requires a lower bound for the dot radius R 0 .…”

Depletion-mode quantum dots in intrinsic silicon

“…These benefits have attracted much attention [6][7][8][9][10][11] to quantum dots (QDs) in group IV material systems as a framework for a solid-state scalable spin-based quantum computer 12 . Recently hole transport in QDs became a subject of particular interest, both experimental [13][14][15][16][17][18][19] and theoretical [20][21][22] , since the hyperfine interaction is strongly suppressed, while the spinorbit coupling enables all-electrical spin manipulation 23 boosting scalability of hole-based qubits. However, enabled electrical spin control makes them vulnerable to charge noise that leads to dephasing and decoherence of the spin states.…”

“…These benefits have attracted much attention 6-11 to quantum dots (QDs) in group IV material systems as a framework for a solid-state scalable spin-based quantum computer 12 . Recently hole transport in QDs became a subject of particular interest, both experimental 13-19 and theoretical [20][21][22] , since the hyperfine interaction is strongly suppressed, while the spinorbit coupling enables all-electrical spin manipulation 23 …”