Resonant hole states in a quantum well with semimagnetic barriers

Theoretical calculations of the valence-band electron states in a two-dimensional quantum well (QW) with diluted magnetic semiconductor barriers are performed in the case of in-plane external magnetic field B. Cases of relatively weak and strong magnetic fields should be discriminated. In the first case the barrier continuum spectrum is separated from localized heavy- and light-hole states in a QW. In the case of a strong enough magnetic field, the superimposition of a barrier continuum spectrum on light-hole QW levels can take place due to the giant spin splitting of semimagmetic semiconductor band states. Moreover, the strong mixing between quantum-confined and barrier states takes place due to the nonconservation of angular momentum in an inclined magnetic field. This results in the transformation of light-hole-localized states in a QW to resonant (virtual) ones. We use a Luttinger model with a symmetric rectangular potential to recapture the transition from localized to resonant states with an increasing external magnetic field B. Calculations of electron-hole optical transitions show a broadening of optical lines and a shift of their maxima. The considered situation is shown to be easily realized in the structures ${\mathrm{Cd}}_{1-x}{\mathrm{Mn}}_x{\mathrm{T}\mathrm{e}/\mathrm{C}\mathrm{d}\mathrm{T}\mathrm{e}/\mathrm{C}\mathrm{d}}_{1-x}{\mathrm{Mn}}_x\mathrm{Te}.$