Quenching of asymmetry-induced spontaneous spin splitting in p-type quantum wells by an applied magnetic field

The spin splitting in the valence band in an ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}/{\mathrm{In}}_x{\mathrm{Ga}}_{1-x}{\mathrm{As}}_y{\mathrm{P}}_{1-y}$ quantum well is investigated theoretically using a $6\times 6$ Luttinger-Kohn Hamiltonian. We compare the Landau levels in a perpendicular magnetic field with the corresponding results for the subband dispersions. It is shown that the asymmetry of the quantum well has a very small impact on the Landau level splitting except for quite small magnetic fields. This is in sharp contrast to the subbands in the absence of a magnetic field. It is suggested that the standard interpretation of Shubnikov–de Haas experiments in terms of hole spin subband populations requires a closer analysis.