Energy spectra and photoluminescence of fractional quantum Hall systems containing a valence-band hole

The energy spectrum of a two-dimensional electron gas (2DEG) interacting with a valence-band hole is studied in the high magnetic field limit as a function of the filling factor ν and the separation d between the electron and hole layers. For d smaller than the magnetic length λ, the hole binds one or more electrons to form neutral (X) or charged (X−) excitons. The low-lying states can be understood in terms of Laughlin-like correlations among the constituent charged fermions (electrons and X−). For d comparable to λ, the electron–hole interaction is not strong enough to bind a full electron, and fractionally charged excitons hQEn (bound states of a hole and one or more Laughlin quasielectrons, QE) are formed. The effect of these excitonic complexes on the photoluminescence spectrum is studied numerically for a wide range of values of ν and d.