  We theoretically consider the effect of plasmon collective modes on the
frequency-dependent conductivity of graphene in the presence of the random
static potential of charged impurities. We develop an equation of motion
approach suitable for the relativistic Dirac electrons in graphene that allows
analytical high-frequency asymptotic solution in the presence of both disorder
and interaction. We show that the presence of the acoustic plasmon pole (i.e.
the plasmon frequency vanishing at long wavelengths as the square-root of
wavevector) in the inverse dynamical dielectric function of graphene gives rise
to a strong variation with frequency of the screening effect of the
relativistic electron gas in graphene on the potential of charged impurities.
The resulting frequency-dependent impurity scattering rate gives rise to a
broad peak in the frequency-dependent graphene optical conductivity with the
amplitude and the position of the peak being sensitive to the detailed
characteristics of disorder and interaction in the system. This sample (i.e.
disorder, elecron density and interaction strength) dependent redistribution of
the spectral weight in the frequency-dependent graphene conductivity may have
already been experimentally observed in optical measurements.
