Interaction effects in the optical conductivity of bilayer graphene: Drude-interband coupling and screening

We present a theory of the influence of band renormalization and excitonic electron-electron interaction effects on the optical conductivity sigma(omega) of doped bilayer graphene. Using the Keldysh formalism, we derive a kinetic equation from which we extract numerical and approximate analytic results for sigma(omega). Our calculations reveal a previously unrecognized mechanism which couples the Drude and interband response and renormalizes the plasmon frequency, and suggest that screening must play an essential role in explaining the weakly renormalized conductivity seen in recent experiments.