Electron–hole systems in narrow quantum wells: excitonic complexes and photoluminescence

The energy and photoluminescence (PL) spectra of a two-dimensional electron gas (2DEG) interacting with a valence-band hole are 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 (X0) or charged (X−) excitons, and PL probes the lifetime and binding energies of these complexes rather than the original correlations of the 2DEG. The low-lying states can be understood in terms of Laughlin-type correlations among the constituent negatively charged Fermions (electrons and X−ʹs). For d, large compared to λ, the electron–hole interaction is not strong enough to bind a full electron, and fractionally charged excitons hQEn (bound states of the hole and one or more Laughlin quasielectrons) are formed. The PL selection rule associated with rotational invariance (conservation of L) is only weakly violated in the interacting plasma, and the position and oscillator strengths of PL lines can be predicted and compared with numerical calculations.