Energy spectra and photoluminescence of charged magneto-excitons

Charged magneto-excitons X− in a dilute 2D electron gas in narrow and symmetric quantum wells are studied using exact diagonalization techniques. An excited triplet X− state with a binding energy of about 1~meV is found. This state and the singlet are the two optically active states observed in photoluminescence (PL). The interaction of X−ʹs with electrons is shown to have short range, which effectively isolates bound X− states from a dilute e–h plasma. This results in the insensitivity of PL to the filling factor ν. For the “dark” triplet X− ground state, the oscillator strength decreases exponentially as a function of ν−1 which explains why it is not seen in PL.