Quadratic response theory for spin-orbit coupling in semiconductor heterostructures

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.