Charged excitons in a dilute two-dimensional electron gas in a high magnetic field

A theory of charged excitons X^- in a dilute two-dimensional (2D) electron gas in a high-magnetic field is presented. In contrast to previous calculations, three bound X^- states (one singlet and two triplets) are found in a narrow and symmetric GaAs quantum well. The singlet and a ``bright'' triplet are the two optically active states observed in experiments. The bright triplet has the binding energy of about 1 meV, smaller than the singlet and a ``dark'' triplet. The interaction of bound X^-'s with a dilute 2D electron gas is investigated using exact diagonalization techniques. It is found that the short-range character of the e--X^- interactions effectively isolates bound X^- states from a dilute $e--h$ plasma. This results in the insensitivity of the photoluminescence spectrum to the filling factor ν, and a rapid decrease of the oscillator strength of the dark triplet X^- as a function of ν^-1.