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

Many semiconductor nanostructures are made from planar two-dimensional heterojunction systems. With a view to merging semiconductor physics, spintronics, and quantum computing, strongly spin-orbit coupled systems such as semiconductor holes have generated burgeoning research interest. While recent experiments in various low-dimensional hole systems have shown great promise in achieving electrical spin control, a thorough understanding of spin-orbit interactions in holes is lacking. Owing to the intricate interactions between holes and their environment, calculations on two-dimensional holes in semiconductor heterojunctions have hitherto always been numerical and material specific, and thus are not easily generalizable to other material systems. In this work, the authors exploit the variational method, k.p perturbation theory, and the theory of invariants to derive general, semianalytical expressions for the spin-orbit interaction in semiconductor heterojunctions. In particular, the authors systematically evaluate the dependence of the Rashba and Dresselhaus spin-orbit interactions on experimental parameters such as material, hole density, and background dopant type. The authors show that the semianalytical approach is easily generalizable to various materials, and present results for common semiconductors GaAs, Ge, InSb, InAs, and Si. Furthermore, the semianalytical results yield good agreement with existing numerical as well as experimental findings.