An exciton in a quantum well in the presence of crossed electric and magnetic fields

Abstract

An analytical approach to the problem of the Wannier–Mott exciton in a semiconductor quantum well (QW) in the presence of external magnetic and electric fields is developed. The magnetic field is taken to lie in the heteroplanes while the electric field is directed perpendicular to the heteroplanes. Explicit dependencies of the energy levels and wave-functions of the exciton on the magnitudes of the fields for a wide range of the width of the QW are obtained. For the narrow QW, the results are valid for arbitrary electron and hole effective masses. In the case of intermediate and wide QWs, the adiabatic approximation implying the extreme difference of the electron and hole masses is used. In the intermediate QW, the states of the relative motion are the standard Coulomb states affected by the external fields while the states of the centre of mass are the size-quantized states in the QW. We focus particularly on the delocalized states caused by the external electric field and the motion of the excitons centre of mass in the magnetic field. These states are localized far away from the Coulomb centre. A strong influence of the boundaries of the wide QW on the delocalized exciton states is found to occur. Estimates of the expected values are made using typical parameters associated with GaAs QW.