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 $X^{-}\mathrm{’}\mathrm{s}$ 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 $\nu ,$ and a rapid decrease of the oscillator strength of the dark triplet $X^{-}$ as a function of ${\nu }^{-1}.$