One-dimensional model of many-exciton effects in photoluminescence spectra
We solve numerically in one dimension and in the self-consistent ladder approximation the many-body problem of interacting electrons and holes. The model contains the minimal ingredients allowing to take into account the coexistence of a population of bound excitonic states with weakly correlated e-h pairs. A simplified contact potential for the Coulomb interaction is used. The strong e-h correlation leads to asymmetric single particle spectral functions with structures related to bound excitonic states. This asymmetry becomes more pronounced at low temperature when the formation of a dense exciton gas occurs. We discuss the role of the many-exciton effects by comparing the photoluminescence peak energies obtained in the ladder and Hartree-Fock approximation.