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

The dynamical dielectric function of two-dimensional graphene at arbitrary wave vector $q$ and frequency $\omega$, $ϵ(q,\omega )$, 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 $(q\to 0)$, the plasmon dispersion shows the local classical behavior ${\omega }_{\mathit{cl}}={\omega }_0\sqrt{q}$, but the density dependence of the plasma frequency $({\omega }_0\propto n^{1∕4})$ is different from the usual 2D electron system $({\omega }_0\propto n^{1∕2})$. The wave-vector-dependent plasmon dispersion and the static screening function show very different behavior than the usual 2D case. We show that the intrinsic interband contributions to static graphene screening can be effectively absorbed in a background dielectric constant.

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Figure 1

(Color online) (a) Plasmon mode dispersion in 2D graphene (solid thick line) calculated within RPA. The dashed line indicates the local long-wavelength plasmon dispersion. Thin solid lines represent the boundaries of the single-particle excitation (SPE) Landau damping regime for intra- and interband electron-hole excitations. (b) The plasmon dispersion and SPE for a normal 2D system with a quadratic energy dispersion.

Figure 2

Static polarizability for 2D graphene: ${\Pi }_{\mathit{tot}}={\Pi }^{+}+{\Pi }^{-}$. Here $\Pi \left(0\right)=D\left(E_F\right)=g_s{g}_v{k}_F∕2\pi \gamma$.