  Semiconductor-superconductor heterostructures represent a promising platform
for the detection of Majorana zero modes and subsequently the processing of
quantum information using their exotic non-Abelian statistics. Theoretical
modeling of such low-dimensional semiconductors is generally based on
phenomenological effective models. However, a more microscopic understanding of
their band structure and, especially, of the spin-orbit coupling of electrons
in these devices is important for optimizing their parameters for applications
in quantum computing. In this paper, we approach this problem by first
obtaining a highly accurate effective tight-binding model from ab initio
calculations in the bulk. This model is symmetrized and correctly reproduces
both the band structure and the wavefunction character. It is then used to
determine Dresselhaus and Rashba spin-orbit splittings induced by finite size
effects and external electric field in zincblende InSb one- and two-dimensional
nanostructures as a function of growth parameters. The method presented here
enables reliable simulations of realistic devices, including those used to
realize exotic topological states.
