  Subband occupancy (i.e. the number of occupied subbands or energy levels in
the semiconductor) is a key physical parameter characterizing the topological
properties of superconductor-semiconductor hybrid systems in the context of the
search for non-Abelian Majorana zero modes. We theoretically study the subband
occupation of semiconductor nanowire devices as function of the applied gate
potential, the semiconductor-superconductor (SM-SC) work function difference,
and the surface charge density by solving self-consistently the
Schr\"{o}dinger-Poisson equations for the conduction electrons of the
semiconductor nanowire. Realistic surface charge densities, which are
responsible for band bending, are shown to significantly increase the number of
occupied subbands, making it difficult or impossible to reach a regime where
only a few subbands are occupied. We also show that the energy separation
between subbands is significantly reduced in the regime of many occupied
subbands, with highly detrimental consequences for the realization and
observation of robust Majorana zero modes. As a consequence, the requirements
for the realization of robust topological superconductivity and Majorana zero
modes should include a low value of the chemical potential, consistent with the
occupation of only a few subbands. Finally, we show that the local density of
states on the exposed nanowire facets provides a powerful tool for identifying
a regime with many occupied subbands and is capable of providing additional
critical information regarding the feasibility of Majorana physics in
semiconductor-superconductor devices. In our work, we address both InAs/Al and
InSb/Al superconductor-nanowire hybrid systems of current experimental
interest.
