Spin splitting in p-type semiconductor nanowires is strongly affected by the interplay between quantum confinement and spin-orbit coupling in the valence band. The latter's particular importance is revealed in our systematic theoretical study presented here, which has mapped the range of spin-orbit coupling strengths realized in typical semiconductors. Large controllable variations of the g-factor with associated characteristic spin polarization are shown to exist for nanowire subband edges, which therefore turn out to be a versatile laboratory for investigating the complex spin properties exhibited by quantum-confined holes.Engineering spin splitting of charge carriers in semiconductor nanostructures may open up intriguing possibilities for realizing spin-based electronics 1 and quantum information processing. 2 Due to the generally strong dependence of g-factors on band structure, 3 it is expected that spatial confinement will have an important effect on Zeeman splitting when bound-state quantization energies are no longer negligible compared with the separation of bulk-material energy bands. The degeneracy of heavy-hole (HH) and light-hole (LH) bulk dispersions at the zone center makes the spin properties of valence-band states especially susceptible to such confinement engineering. 4,5,6,7 Recent advances in fabrication technology 8,9,10,11,12,13,14,15,16 have created opportunities to investigate hole spin physics in semiconductor nanowires made from a range of different materials.In contrast to previous theoretical work 17,18,19,20 on hole spin splitting in quantum wires, we focus here on the influence of the spin-orbit coupling strength on Zeeman splitting of wire-subband edges. A suitable parameter γ quantifying spin-orbit coupling in the valence band can be defined in terms of the effective masses m HH and m LH associated with the HH and LH bands, 21 respectively: 2γ = (m HH − m LH )/ (m HH + m LH ). Table I lists values for γ in common semiconductors and states its relation to basic bandstructure parameters. 22 A large part of the theoretically possible range 0 ≤ γ ≤ 1/2 is covered by available materials, 23 enabling a detailed study of the interplay between spin-orbit coupling in the valence band and nanowire confinement. Our theoretical investigation reveals surprising qualitative differences in the hole spin properties of nanowires depending on the value of γ, showing that spin splitting (and polarization) of zone-center valence-band edges in nanowires is highly tunable and has a complex materials dependence. A detailed understanding of these properties is vital for proper interpretation of optical and transport measurements as well as for the design of spintronic applications involving p-doped semiconductor nanowires.We use the Luttinger model 22 in the spherical approximation 26 for the top-most bulk valence bands. Including the bulk Zeeman term H Z = −2κµ B BĴ z , the Hamiltonian is given byHere p is the linear orbital momentum,Ĵ the vector of spin-3/2 matrices, m 0 the electron mass in vacuum, γ ...