Full-zone spin-splitting for electrons and holes in bulk GaAs and GaSb

TLDR: In this article, the authors provided a full-zone description of the Dresselhaus splitting in zinc blende semiconductors by using pseudopotentials, empirically corrected to rectify local density approximation errors by fitting $GW$ results.

Abstract: The spin-orbit interaction---a fundamental electroweak force---is equivalent to an effective magnetic field intrinsic to crystals, leading to band spin splitting for certain $k$ points in sufficiently low-symmetry structures. This (Dresselhaus) splitting has usually been calculated at restricted regions in the Brillouin zone via small wave vector approximations (e.g., $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$), potentially missing the ``big picture.'' We provide a full-zone description of the Dresselhaus splitting in zinc blende semiconductors by using pseudopotentials, empirically corrected to rectify local density approximation errors by fitting $GW$ results. In contrast to what was previous thought, we find that the largest spin splitting in the lowest conduction band and upper valence band (VB1) occurs surprisingly along the (210) direction, not the (110) direction, and that the splitting of the VB1 is comparable to that of the next two valence bands VB2 and VB3.