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Plasmons in ordinary electron liquids are collective excitations whoselong-wavelength limit is rigid center-of-mass motion with a dispersion relationthat is, as a consequence of Galileian invariance, unrenormalized by many-bodyeffects. The long-wavelength plasmon frequency is related by the f-sum rule tothe integral of the conductivity over the electron-liquid's Drude peak,implying that transport properties also tend not to have importantelectron-electron interaction renormalizations. In this article we demonstratethat the plasmon frequency and Drude weight of the electron liquid in a dopedgraphene sheet, which is described by a massless Dirac Hamiltonian and notinvariant under ordinary Galileian boosts, are strongly renormalized even inthe long-wavelength limit. This effect is not captured by the Random PhaseApproximation (RPA), commonly used to describe electron fluids. It is dueprimarily to non-local inter-band exchange interactions, which, as we show,reduce both the plasmon frequency and the Drude weight relative to the RPAvalue. Our predictions can be checked using inelastic light scattering orinfrared spectroscopy.

Drude weight, plasmon dispersion, and pseudospin response in doped graphene sheets