Variational Rashba splitting in two-dimensional electron gases in III-V semiconductor heterojunctions

Abstract

Control of the Rashba spin-orbit coupling in semiconductor two-dimensional electron gases (2DEGs) is of fundamental interest to the rapidly evolving semiconductor spintronics and depends on the detailed knowledge of the controversial interface and barrier penetration effects. Based on the $8\ifmmode\times\else\texttimes\fi{}8$ $\mathbf{k}\ensuremath{\cdot}\mathbf{p}$ Kane model for the bulk, we propose a spin-dependent variational solution for the conduction subbands of III-V heterojuctions, which reveals analytically the different contributions to the Rashba splitting and its dependency on heterostructure and band parameters as the band offset and effective masses. Perturbation expansions are used to derive renormalized parameters for an effective, simple, and yet accurate one band model. Spin-dependent modified Fang-Howard trial functions, which satisfy the spin-dependent boundary conditions, are then introduced. The subband splitting is given as a function of the variational parameter which is obtained minimizing the total energy of the 2DEG. Our calculations applied to InAlAs/InGaAs heterojunctions, where a near 20% increase in the splitting is observed due to the barrier penetration, are in good agreement with both experiment and exact numerical calculations. Well-known expressions in the limit of a perfect insulating barrier are exactly reproduced.