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

Abstract

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 v 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 hQE _n (bound states of a hole and one or more Laughlin quasi-electrons, QEs) are formed. The effect of these excitonic complexes on the photoluminescence spectrum is studied numerically for a wide range of values of v and d.