The polarization of graphene is calculated exactly within the random phase approximation for arbitrary frequency, wavevector and doping. At finite doping, the static susceptibility saturates to a constant value for low momenta. At q = 2kF it has a discontinuity only in the second derivative. In the presence of a charged impurity this results in Friedel oscillations which decay with the same power law as the Thomas-Fermi contribution, the latter being always dominant. The spin density oscillations in the presence of a magnetic impurity are also calculated. The dynamical polarization for low q and arbitrary ω is employed to calculate the dispersion relation and the decay rate of plasmons and acoustic phonons as a function of doping. The low screening of graphene, combined with the absence of a gap, leads to a significant stiffening of the longitudinal acoustic lattice vibrations. © IOP Publishing Ltd. and Deutsche Physikalische Gesellschaft.
CITATION STYLE
Wunsch, B., Stauber, T., Sols, F., & Guinea, F. (2006). Dynamical polarization of graphene at finite doping. New Journal of Physics, 8. https://doi.org/10.1088/1367-2630/8/12/318
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