Valence-band mixing in first-principles envelope-function theory

Abstract

This paper presents a numerical implementation of a first-principles envelope-function theory derived recently by the author [B. A. Foreman, Phys. Rev. B 72, 165345 (2005)]. The examples studied deal with the valence subband structure of $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{As}$, $\mathrm{Ga}\mathrm{As}∕{\mathrm{Al}}_{0.2}{\mathrm{Ga}}_{0.8}\mathrm{As}$, and ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}\mathrm{As}∕\mathrm{In}\mathrm{P}$ (001) superlattices calculated using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. The heterostructure Hamiltonian is approximated using quadratic-response theory, with the heterostructure treated as a perturbation of a bulk reference crystal. The valence subband structure is reproduced accurately over a wide energy range by a multiband envelope-function Hamiltonian with linear renormalization of the momentum and mass parameters. Good results are also obtained over a more limited energy range from a single-band model with quadratic renormalization. The effective kinetic-energy operator ordering derived here is more complicated than in many previous studies, consisting in general of a linear combination of all possible operator orderings. In some cases, the valence-band Rashba coupling differs significantly from the bulk magnetic Luttinger parameter. The splitting of the quasidegenerate ground state of no-common-atom superlattices has non-negligible contributions from both short-range interface mixing and long-range dipole terms in the quadratic density response.