Gauge-invariant discretization in multiband envelope function theory and g factors in nanowire dots

We present a gauge-invariant discretization scheme for the multiband envelope function approximation including strain as well as relativistic effects. Our procedure is based on Wilson's formulation of gauge theories. The magnetic field couples to the envelope functions via phase factors that result from spatial discretization of the gauge covariant derivative. These phase factors contain a discretized curve integral over the vector potential. In addition, the carrier's spin couples to the magnetic field via a Zeeman term. In the case of infinitesimal grid spacings, our method becomes equivalent to the minimal substitution method. Applying our procedure, we calculate the effective electron and hole g tensor of InAs/InP nanowire dots and obtain excellent agreement with experimental data. We show that the correct momentum operator ordering in the Hamiltonian grossly affects the hole g factors. Furthermore, we investigate the influence of strain on g factors and nonlinear Zeeman splittings in high magnetic fields.