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Paper IPM / P / 11373  


Abstract:  
Plasmon in ordinary electron liquids are collective excitations whose longwavelength limit is a rigid centerofmass motion with a dispersion relation that is, as a consequence of Galileian invariance, unrenormalized by manybody effects. The longwavelength plasmin frequency is related by the fsum rule to the integral of the conductivity over the electronliquid's Drude peak, implying that transport properties also tend not to have important electronelectron interaction renormalizations. In this article we demonstrate that the palsmon frequency and Drude weight of the electronliquid in a doped graphene sheet  which  is described by a massless Dirac Hamiltonian and not invariant under ordinary Galileian boostsare strongly renormalized even in the longwavelength limit. This effect is not captured by the Random Phase Approximation (RPA), commonly used to describe electron fluids. It is due to the coupling between the center of mass motion and the pseudospin degree of freedom of the massless Dirac fermions. We show that this coupling enhances 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.
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