A functional approach to polariton quantum crystals

We study a generalized Dicke model of polaritons, with a pair-potential interaction between excited states of the spin component, in the functional integral formalism. With a potential that is attractive over a finite momentum range and otherwise repulsive, we determine stability conditions for a spatially homogeneous state. We find that depending on the potential, the interaction may induce an instability in the sound mode of the polariton condensate, or destroy the condensate altogether. In the case of an instability, we study the existence and excitations of weakly periodic states in a triangular lattice.