Using a nonlinear Schrödinger equation including short-range two-body attraction and three-body repulsion, we investigate the spatial distribution of indirect excitons in semiconductor coupled quantum wells. The results obtained can explain the experimental phenomenon that the annular exciton cloud first contracts then expands when the number of confined excitons is increased in the impurity potential well, as observed by Lai et al (2004 Science 303 503). In particular, the model reconciles the patterns of exciton rings reported by Butov et al (2002 Nature 418 751). At higher densities, the model predicts much richer patterns, which could be tested by future experiments.
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