Dielectric function, screening, and plasmons in two-dimensional graphene

The dynamical dielectric function of two-dimensional graphene at arbitrary wave vector $q$ and frequency $\ensuremath{\omega}$, $ϵ(q,\ensuremath{\omega})$, is calculated in the self-consistent-field approximation. The results are used to find the dispersion of the plasmon mode and the electrostatic screening of the Coulomb interaction in two-dimensional (2D) graphene layer within the random-phase approximation. At long wavelengths $(q\ensuremath{\rightarrow}0)$, the plasmon dispersion shows the local classical behavior ${\ensuremath{\omega}}_{\mathit{cl}}={\ensuremath{\omega}}_{0}\sqrt{q}$, but the density dependence of the plasma frequency $({\ensuremath{\omega}}_{0}\ensuremath{\propto}{n}^{1∕4})$ is…