Dielectric function, screening, and plasmons in 2D graphene

TL;DR

This paper calculates the dielectric function, plasmon dispersion, and screening properties of 2D graphene, revealing unique wave vector and density dependencies that differ from traditional 2D electron systems.

Contribution

It provides a comprehensive analysis of the dielectric response and plasmon behavior in graphene at arbitrary wave vectors and frequencies, highlighting novel dispersion and screening characteristics.

Findings

Plasmon dispersion follows a classical $ oot{q}$ behavior at long wavelengths.

The plasma frequency scales with density as $n^{1/4}$, unlike conventional 2D systems.

Screening functions exhibit distinct behavior from typical 2D electron gases.

Abstract

The dynamical dielectric function of two dimensional graphene at arbitrary wave vector $q$ and frequency $\omega$, $\epsilon(q,\omega)$, 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 2D graphene layer within the random phase approximation. At long wavelengths ($q\to 0$) the plasmon dispersion shows the local classical behavior $\omega_{cl} = \omega_0 \sqrt{q}$, 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.