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Photoluminescence of the incompressible Laughlin liquid: Excitons, charged excitons, and fractionally charged excitons

The photoluminescence (PL) of a two-dimensional electron gas (2DEG) in a high magnetic field is studied as a function of the filling factor and the separation d between the electron layer and the valence hole. Depending on the magnitude of d relative to the magnetic length lambda, two distinct regimes in the response of the 2DEG to the valence hole occur, with different elementary emission processes contributing to the PL spectrum. At d<lambda ("strong coupling" regime), the hole binds one or two electrons to form an exciton (X) or one of three possible charged exciton (X-) states, a spin-singlet or one of two spin-triplets. At d>lambda ("weak coupling" regime), the hole decouples or binds one or two Laughlin quasielectrons to form fractionally charged excitons (FCX's). The binding energies as well as the emission energies and intensities of all X- and FCX states are calculated.