Ab-initio Prediction of Conduction Band Spin Splitting in Zincblende Semiconductors

We use a recently developed self-consistent $GW$ approximation to present systematic \emph{ab initio} calculations of the conduction band spin splitting in III-V and II-V zincblende semiconductors. The spin orbit interaction is taken into account as a perturbation to the scalar relativistic Kohn-Sham hamiltonian. These are the first calculations of conduction band spin splittings based on a quasiparticle approach. We show that the self-consistent $GW$ scheme accurately reproduces the relevant band parameters, and is therefore expected to be a reliable predictor of spin splittings. The results are compared to the few available experimental data and a previous calculation based on a model one-particle potential. We show that the commonly used ${\bf{}k}\cdot{\bf{}p}$ hamiltonian is missing contributions, and cannot reliably reproduce the splittings.