Electron-electron interactions and plasmon dispersion in graphene

Plasmons in two-dimensional electron systems with nonparabolic bands, such as graphene, feature strong dependence on electron-electron interactions. We use a many-body approach to relate plasmon dispersion at long wavelengths to Landau Fermi-liquid interactions and quasiparticle velocity. An identical renormalization is shown to arise for the magnetoplasmon resonance. For a model with $N\gg 1$ fermion species, this approach predicts a power-law dependence for plasmon frequency vs carrier concentration, valid in a wide range of doping densities, both high and low. Gate tunability of plasmons in graphene can be exploited to directly probe the effects of electron-electron interaction.

Figure 1

Resummed Feynman graphs for the polarization operator $\Pi (\mathbf{q},\omega )$. The non-quasiparticle contribution ${\Pi }_0(\mathbf{q},\omega )$ and the FL ladder ${\sum }_{n\ge 1}{\Pi }_n(\mathbf{q},\omega )$ are shown. Only the contributions ${\Pi }_1(\mathbf{q},\omega )$ and ${\Pi }_2(\mathbf{q},\omega )$ contribute to the low-energy plasmon dispersion; see text.

Figure 2

Feynman graphs for the “quasiparticle-irreducible” quantities ${\mathcal{T}}^{\omega },{\Gamma }^{\omega }$. The bold lines represent a full Green's function, the thin lines represent a singular part $G^{\left(\mathrm{sing}\right)}$. The vertex ${\Gamma }_0$ represents the conventional irreducible vertex, whereas hatched blocks represent products of two Green's functions, with the contributions $G^{\left(\mathrm{sing}\right)}{G}^{\left(\mathrm{sing}\right)}$, which give a nonanalytical behavior at small $\omega ,\mathbf{q}$, taken out (see text).