Theory ofX−at high magnetic fields

We calculate, to high accuracy, the states of the quantum-well negatively charged exciton $X^{-}$ in a perpendicular magnetic field. Two GaAs structures are considered: a 100-Å “narrow” well and a 300-Å “wide” well. The calculations cover a magnetic field range from 5 T to 50 T. In the narrow well, the ground state is shown to switch from singlet to triplet, at about 30 T, in agreement with the prediction of a triplet ground state obtained using the lowest-Landau-level approximation. In the wide well, the singlet is still the ground state at 50 T because electron-hole correlations perpendicular to the well plane enhance its binding energy more than that of the triplet. We also calculate electron-electron correlation functions for the $X^{-}$ states and demonstrate that in the singlet the motions of the two electrons are correlated, while in the triplet they are anticorrelated. We show that the triplet binding energies in the wide well are in good agreement with experimental data; the singlet values, however, turn out to be considerably smaller than those measured.