  Full-shell hybrid nanowires (NWs), structures comprising a superconductor
shell that encapsulates a semiconductor (SM) core, have attracted considerable
attention in the search for Majorana zero modes (MZMs). The main caveats of
this platform, however, are that the predicted Rashba spin-orbit coupling (SOC)
in the SM is too small to achieve substantial topological minigaps and that the
MZMs typically coexist with a finite background of trivial subgap states. In
order to overcome both problems, we explore the advantages of utilizing
core-shell hole-band NWs for the SM part of the full-shell hybrid, with an
insulating core and an active SM shell. In particular, we consider InP/GaSb
core-shell NWs, which allow to exploit the unique characteristics of the III-V
compound SM valence bands. We demonstrate that they exhibit a robust hole SOC
that depends mainly on SM and geometrical parameters. In other words, the SOC
is intrinsic and does not rely on neither electric fields, which are
non-tunable in a full-shell hybrid geometry, nor on the strain at the
interface, contrary to what happens in Ge/Si heterostructures where the strain
plays a crucial role. As a result, core-shell hole-band NWs emerge as a
promising candidate for full-shell Majorana physics, addressing several
challenges in the field.
