Effect of free carriers and impurities on density of states and optical spectra of two-dimensional magneto-excitons

Density of states (DOS) and absorption spectrum of weakly doped, narrow quantum wells in high magnetic fields are calculated by realistic exact diagonalization. The systems containing an electron--hole pair with and without an additional, second electron are compared. In DOS, the exciton--electron interaction is shown to fill the gaps between Landau levels and to yield additional discrete peaks corresponding to bound trion states. In absorption, interaction with the additional free electron causes no shift or renormalization of main, excitonic peaks. However, it results in additional, weaker peaks associated with bound trions in the lowest or higher Landau levels. The calculation is supplemented with experimental photoluminescence and photoluminescence-excitation studies of two-dimensional holes and electrons in high magnetic fields.