Quantum confinement effects on the spin splitting and polarization of quasi-1D holes

We study spin splitting and polarization of hole subband edges in nanowires with cylindrical and square cross-section in the presence of a magnetic field applied along the wire direction. A general feature of the interplay between quantum confinement and the strong spin–orbit coupling in the valence band is that the g-factors of the hole–wire bound states fluctuate strongly as a function of level index. In addition, they are suppressed in comparison to g  -factors found in higher-dimensional systems. We analyze the hole–spin properties of the wire levels in terms of invariants of the spin-32 density matrix and discuss effects of confinement and geometry on the hole–spin polarization and its correlation to the g-factor values.