  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 GaAs/AlAs, GaAs/Al(0.2)Ga(0.8)As, and In(0.53)Ga(0.47)As/InP (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.
