Bethe-Salpeter equation for magnetoexcitons in quantum wells

We study the problem of an exciton in a quantum well in the presence of a strong external constant magnetic field directed normal to the layers. Our approach is based on the nonrelativistic Bethe-Salpeter equation for the two-particle bound state in the presence of a magnetic field. We obtain that the recently predicted phenomenon of the magnetic catalysis in QED and QCD also takes place in exciton physics: the homogeneous magnetic field induces an energy gap in the exciton spectrum. The ground-state energies of heavy- and light-hole magnetoexcitons in GaAs/AlGaAs quantum wells are calculated by solving the Bethe-Salpeter equation in the lowest Landau level approximation. The calculated energies are in agreement with photoluminescence and photoconductivity spectra of very thin GaAs/AlGaAs quantum wells at different magnetic fields of up to 20 T.