Zeeman splitting in cylindrical hole quantum wires

We have investigated the effect of one-dimensional (1D) confinement on the Zeeman splitting of holes in cylindrical quantum wires for magnetic fields applied parallel to the wire axis. Our theoretical study is based on the Luttinger–Hamiltonian description for the valence band in the spherical approximation. We obtain exact results for energies and Landé g-factors of hole states at the quasi-1D subband edges. The g-factor values are universal in the sense that they only depend on the subband index but not on the wire dimensions. Strong fluctuations are observed among the g-factors for low-lying subband edges, and their specific values are unexpected for a situation when the magnetic field is applied parallel to an axis of high symmetry that could naively be equated with the quantisation axis of total angular momentum. It appears that the requirement of a single-valued hole wave function associated with cylindrical symmetry induces a strong mixing between heavy and light holes, which results in the observed behaviour.