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There is a rich variety of quantum liquids -- such as superconductors, liquid helium and atom Bose-Einstein condensates -- that exhibit macroscopic coherence in the form of ordered arrays of vortices. Experimental observation of a macroscopically ordered electronic state in semiconductors has, however, remained a challenging and relatively unexplored problem. A promising approach for the realization of such a state is to use excitons, bound pairs of electrons and holes that can form in semiconductor systems. At low densities, excitons are Bose-particles, and at low temperatures, of the order of a few kelvin, excitons can form a quantum liquid -- that is, a statistically degenerate Bose gas or even a Bose-Einstein condensate. Here we report photoluminescence measurements of a quasi-two-dimensional exciton gas in GaAs/AlGaAs coupled quantum wells and the observation of a macroscopically ordered exciton state. Our spatially resolved measurements reveal fragmentation of the ring-shaped emission pattern into circular structures that form periodic arrays over lengths up to 1 mm.

Macroscopically ordered state in an exciton system