Formation of an order in a system of exciton condensed phase islands in quantum wells

An electrons and holes of indirect excitons in semiconductor coupled quantum wells are localized in different wells and as the result the excitons have long lifetime. Such system present interest for study of exciton condensation phenomena [1]. Recently interesting experiments were fulfilled for indirect excitons in AlGaAs and InGaAs crystals with coupled quantum wells. In works [2, 3, 4, 5, 6, 7] the authors have observed a ring structure in emission of indirect excitons outside of laser spot. The distance between ring and center of the excitation spot growths with increasing the pumping and can reach several hundred microns that is much larger than the exciton diffusion length. At low temperature (T ≤ 2K) the external ring is fragmented into periodical structure over macroscopic lengths. The mechanism of the luminescence ring formation was proposed in [6, 7]. The origin of fragmentation along the ring is unclear. In present work the appearance of this fragmentation is explained by creation of islands of exciton condensed phases along the ring. In [8, 9] it was shown that in the presence of an attractive interaction between excitons a high density exciton system is unstable with respect to the periodical structure appearance. To obtain the spacial dependence of the exciton generation rate we shall use the suggestion of paper [6, 7] that in absence of the light irradiation the quantum well contains electrons and that holes created by light are captured by quantum well more