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Supersolid versus phase separation in atomic bose-fermi mixtures.

We show that a two-dimensional atomic mixture of bosons and fermions cooled into their quantum degenerate states and subject to an optical lattice develops a supersolid phase characterized by the simultaneous presence of a nontrivial crystalline order and phase order. This transition is in competition with phase separation. We determine the phase diagram of the system and propose an experiment allowing for the observation of the supersolid phase.