Spin-orbit splitting of GaAs and InSb bands near Γ

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Abstract
An ab initio pseudopotential calculation is used to examine the spin-orbit splitting of states in the zinc-blende semiconductors GaAs and InSb within the local-density approximation (LDA). The relativistic pseudopotentials are generated with the occupied d orbitals of the atoms in the rigid core. No correction is made to the calculated band gaps even though they are too small as a result of the LDA, resulting in a semimetal for InSb. These two features differ from an earlier ab initio linear muffin-tin orbitals (LMTO) calculation in which mixing of the d core states was included and the gap was corrected empirically. We examine the spin-orbit splitting of the valence bands at point Γ, and the linear-in-‖k‖ splitting and mixing of the upper valence bands for the [100], [111], and [110] directions in a small region around point Γ. This provides a detailed calculation of the splitting and mixing of the light- and heavy-hole valence bands in the region of near-degeneracy. We also examine the linear and cubic terms away from point Γ in the [110] direction where the light and heavy holes are separated in energy and do not intermix appreciably. The spin-orbit splittings and linear-in-‖k‖ valence-band splittings are in excellent agreement with the LMTO calculation and with experiment; however, an error in earlier analyses regarding the relative sign of two linear terms is found. The cubic terms are, for the most part, not accurate, which is expected from a local-density-functional calculation.