Theory of magnetoexcitons in quantum wells

Abstract

The properties of excitons in GaAs/${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As quantum wells in the presence of magnetic fields up to 10 T are calculated in an effective-mass approximation. The valence bands are represented by the Luttinger Hamiltonian and the penetration of the exciton wave function into the barrier is taken into account. Hole-band mixing is found to cause significant effects like a sizable (ca. 20%) paramagnetic contribution to the exciton diamagnetic shift. The theoretical results compare well with high-resolution magnetoluminescence spectra by Ossau and co-workers. In agreement with experiment we find for example a small spin splitting of the heavy-hole exciton which changes sign at intermediate magnetic fields.