Drude weight, plasmon dispersion, and a.c. conductivity in doped graphene sheets

We demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet are strongly renormalized by electron-electron interactions even in the long-wavelength limit. This effect is not captured by the random-phase approximation (RPA), commonly used to describe electron fluids, and is due to coupling between the center-of-mass motion and the pseudospin degree of freedom of the graphene's massless Dirac fermions. By making use of diagrammatic perturbation theory to first order in the electron-electron interaction, we show that this coupling enhances both the plasmon frequency and the Drude weight relative to the RPA value. We also show that interactions are responsible for a significant enhancement of the optical conductivity at frequencies just above the absorption threshold. Our predictions can be checked by far-infrared spectroscopy or inelastic light scattering.