Theory of band gap renormalisation in modulation-doped quantum wells

The frequency of the photoluminescence radiation in modulation-doped quantum wells is theoretically investigated. The vertex correction which describes the effect of the interaction between the annihilating electron-hole pairs is shown to be negligible. Consequently the emission frequency is determined by the fundamental band gap, which requires the calculation of the self-energies of the valence band holes and the conduction band electrons. These calculations are carried out perturbationally using the plasmon-pole approximation for the dielectric function and variationally determined gaussian-type envelope functions. The electron and hole energy levels are also calculated self-consistently by local-density functional theory. The results of both theories agree with each other over a large range of conduction electron densities and explain recent experiments well.