Resonance impurity states in a quantum well in the presence of electric and strong magnetic fields

An analytical approach to the problem of an impurity electron (or hole) in a quantum well (QW), subject to electric and strong magnetic external fields both directed perpendicular to the heteroplanes, is developed. The impurity center is located at the edge of the QW. It is shown that the combined potential acting on the electron (or hole) resembles that of a double quantum well. One of the wells is formed by the Coulomb impurity potential and the QW boundary at which the center is located and the other well by the electric-field potential and the other boundary of the well. Analytical expressions for the energy levels are obtained. Our main interest is in the resonance when the levels associated with the two effective QW's anticross. The explicit dependences of the resonance splitting upon the width of the QW and on the magnitudes of the electric and magnetic fields are obtained. Estimates of the expected splittings are made using the usual parameters associated with GaAs QW"s.