Pattern formation of indirect excitons in coupled quantum wells

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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 interpret the experimental phenomenon that annular exciton cloud first contracts then expands when the number of confined excitons is increased in impurity potential well, as observed by Lai et al. [Lai et al., Science 303, 503 (2004)]. In particular, the model reconciles the patterns of exciton rings reported by Butov et al. [Butov et al., Nature 418, 751 (2002)]. At higher densities, the model predicts much richer patterns, which could be tested by future experiments.