  This paper examines the properties of the self-energy operator in
lattice-matched semiconductor heterostructures, focusing on nonanalytic
behavior at small values of the crystal momentum, which gives rise to
long-range Coulomb potentials. A nonlinear response theory is developed for
nonlocal spin-dependent perturbing potentials. The ionic pseudopotential of the
heterostructure is treated as a perturbation of a bulk reference crystal, and
the self-energy is derived to second order in the perturbation. If spin-orbit
coupling is neglected outside the atomic cores, the problem can be analyzed as
if the perturbation were a local spin scalar, since the nonlocal spin-dependent
part of the pseudopotential merely renormalizes the results obtained from a
local perturbation. The spin-dependent terms in the self-energy therefore fall
into two classes: short-range potentials that are analytic in momentum space,
and long-range nonanalytic terms that arise from the screened Coulomb potential
multiplied by a spin-dependent vertex function. For an insulator at zero
temperature, it is shown that the electronic charge induced by a given
perturbation is exactly linearly proportional to the charge of the perturbing
potential. These results are used in a subsequent paper to develop a
first-principles effective-mass theory with generalized Rashba spin-orbit
coupling.

Materials Science