Using a nonlinear Schr\"odinger 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 \emph{et al.} [Lai etal., Science \textbf{303}, 503 (2004)]. In particular, the model reconciles the patterns of exciton rings reported by Butov \emph{et al.} [Butov etal., Nature \textbf{418}, 751 (2002)]. At higher densities, the model predicts much richer patterns, which could be tested by future experiments.
@article{arxiv.cond-mat/0604564,
title = {Pattern formation of indirect excitons in coupled quantum wells},
author = {C. S. Liu and H. G. Luo and W. C. Wu},
journal= {arXiv preprint arXiv:cond-mat/0604564},
year = {2009}
}