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 ($\omega \tau \gg 1$ where $\tau$ is the scattering time) in the presence of both disorder and interaction. We show that the presence of the gapless plasmon pole (in graphene the plasmon frequency vanishes at long wavelengths as the square root of wave number) 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-dependent (i.e., disorder, electron density, and interaction strength) redistribution of the spectral weight in the frequency-dependent graphene conductivity may have already been experimentally observed in optical measurements.

• Received 28 May 2013

DOI:https://doi.org/10.1103/PhysRevB.88.085403