Valence-band levels and optical transitions in quantum wells in a parallel magnetic field

The magnetic hole levels of GaAs/${\mathrm{Al}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ga}}_{\mathrm{x}}$As quantum wells in a parallel field are computed in the effective-mass approximation, by means of an extension of the Luttinger oscillator formalism to noninteger quantum numbers. A detailed analysis of the valence subbands and their dependence on the well width, magnetic field, and aluminum composition is performed. We also compute the transition energy for different conduction valence subbands in GaAs/${\mathrm{Al}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Ga}}_{\mathrm{x}}$As quantum wells in parallel fields, and compare with recent photoconductivity experiments.