Drude Weight, Cyclotron Resonance, and the Dicke Model of Graphene Cavity QED

The unique optoelectronic properties of graphene make this two-dimensional material an ideal platform for fundamental studies of cavity quantum electrodynamics in the strong-coupling regime. The celebrated Dicke model of cavity quantum electrodynamics can be approximately realized in this material when the cyclotron transition of its 2D massless Dirac fermion carriers is nearly resonant with a cavity photon mode. We develop the theory of strong matter-photon coupling in this circumstance, emphasizing the essential role of a dynamically generated matter energy term that is quadratic in the photon field and absent in graphene's low-energy Dirac model.