Subbands and Landau levels in the two-dimensional hole gas at the GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As interface

The hole subbands and Landau levels in the inversion layer at the interface between GaAs and p-type ${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As are calculated self-consistently in the Hartree approximation. The degenerate valence-band structure and the matching of the wave function at the interface are taken into account. Without magnetic field we calculate the subband dispersion parallel to the interface. The subbands are found to be strongly nonparabolic and spin split. The calculated classical cyclotron effective masses do not agree very well with those found in cyclotron resonance experiments. We have therefore included the magnetic field in the calculation. The B dependence of the Landau levels is found to be strongly nonlinear. The calculated transition energies are partly in very good agreement with experiment. The dependence of the results on areal hole density, doping concentrations, valence-band discontinuity, etc., is also investigated.