Drude weight, cyclotron resonance, and the Dicke model of graphene cavity QED

The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode. We point out that in the strong coupling limit the Dicke model of cavity cyclotron resonance must be supplemented by a term that is quadratic in the cavity photon field and suppresses the model's transition to a super-radiant state. We develop the theory of graphene cavity cyclotron resonance and show that the quadratic term, which is absent in graphene's low-energy Dirac model Hamiltonian, is in this case dynamically generated by virtual inter-band transitions.

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.