Dicke Phase Transition in a Disordered Emitter-Graphene Plasmon System

We study the Dicke phase transition in a disordered system of emitters coupled to the plasmonic modes of a graphene monolayer. This system has unique properties associated with the tunable, dissipative and broadband characters of the graphene surface plasmons, as well as the disorder due to the random spatial distribution and the inhomogeneous line-width broadening of the emitters. We apply the Keldysh functional-integral approach, and identify a normal phase, a superradiant phase and a spin-glass phase of the system. The conditions for these phases and their experimental signatures are discussed.