Drude weight, plasmon dispersion, and pseudospin response in doped graphene sheets
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Plasmons in ordinary electron liquids are collective excitations whose long-wavelength limit is rigid center-of-mass motion with a dispersion relation that is, as a consequence of Galileian invariance, unrenormalized by many-body effects. The long-wavelength plasmon frequency is related by the f-sum rule to the integral of the conductivity over the electron-liquid's Drude peak, implying that transport properties also tend not to have important electron-electron interaction renormalizations. In this article we demonstrate that the plasmon frequency and Drude weight of the electron liquid in a doped graphene sheet, which is described by a massless Dirac Hamiltonian and not invariant under ordinary Galileian boosts, are strongly renormalized even in the long-wavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids. It is due primarily to non-local inter-band exchange interactions, which, as we show, reduce both the plasmon frequency and the Drude weight relative to the RPA value. Our predictions can be checked using inelastic light scattering or infrared spectroscopy.