Unconventional plasmon-phonon coupling in graphene

We predict the existence of coupled plasmon-phonon excitations in graphene by using the self-consistent linear response formalism. The unique electron-phonon interaction in graphene leads to unconventional mixing of plasmon and optical phonon polarizations. We find that longitudinal plasmons couple exclusively to transverse optical phonons, whereas graphene’s transverse plasmons couple only to longitudinal optical phonons. This coupling can serve as a magnifier for exploring the electron-phonon interaction in graphene, and it offers electronical control over phonon frequencies.

Figure 1

(a) Schematic illustration of the lattice structure with two sublattices ($A$ and $B$). (b) The two degenerate Dirac cones are centered at $K$ and $K^{\text{'}}$ points at the edge of the Brillouin zone. (c) A displacement of lattice atoms $\mathbf{u}(\mathbf{r})$ is parallel (perpendicular) to the propagation wave vector $\mathbf{q}$ of a LO (TO) phonon. (d) The displacement $\mathbf{u}(\mathbf{r})$ creates an effective vector potential ${\mathbf{A}}_{\mathrm{eff}}$ perpendicular to $\mathbf{u}(\mathbf{r})$ (the sign of ${\mathbf{A}}_{\mathrm{eff}}$ for the $K^{\text{'}}$ point is opposite to that for the $K$ point).

Figure 2

Dispersion lines of hybrid LP-TO plasmon-phonon modes (solid lines) and of the uncoupled modes (dashed lines) for two values of doping: (a) $n=5\times {10}^{12}$ cm${}^{-2}$ and (b) $n=5\times {10}^{13}$ cm${}^{-2}$. The hybridization is stronger for larger doping values. Gray areas denote the region of single-particle damping.

Figure 3

Dispersion lines of hybrid TP-LO plasmon-phonon modes (solid lines) and of the uncoupled modes (dashed lines) for two values of doping: (a) $n=7.5\times {10}^{11}$ cm${}^{-2}$ and (b) $n=9.5\times {10}^{11}$ cm${}^{-2}$. The plasmonlike dispersion is very close to the light line $q=\omega /c$; therefore, the ordinate shows $\Delta q=q-\omega /c$.