Strong phonon-plasmon coupled modes in the graphene/silicon carbide heterosystem

We report on strong coupling of the charge-carrier plasmon ${\omega }_{PL}$ in graphene with the surface-optical phonon ${\omega }_{SO}$ of the underlying SiC(0001) substrate with low-electron concentration $\left(n=1.2\times {10}^{15}{\text{cm}}^{-3}\right)$ in the long-wavelength limit $\left(q_{\parallel }\to 0\right)$. Energy-dependent energy-loss spectra give clear evidence of two coupled phonon-plasmon modes ${\omega }_{\pm }$ separated by a gap between ${\omega }_{SO}\left(q_{\parallel }\to 0\right)$ and ${\omega }_{\text{TO}}\left(q_{\parallel }⪢0\right)$, the transverse-optical-phonon mode, in particular, for higher primary electron energies $\left(E_0\ge 20\text{eV}\right)$. A simplified model based on dielectric theory is able to simulate our energy-loss spectra as well as the dispersion of the two coupled phonon-plasmon modes ${\omega }_{\pm }$. In contrast, Liu and Willis [Phys. Rev. B 81, 081406(R) (2010)] postulate in their recent publication no gap and a discontinuous dispersion curve with a one-peak structure from their energy-loss data.

Figure 1

Energy-loss spectra in specular direction at a spectrometer resolution of $20{\text{cm}}^{-1}$ on different samples. (a) On hydrogen etched silicon carbide with $E_0=36\text{eV}$ and (b) on the graphene/SiC(0001) heterosystem with $E_0=20\text{eV}$. $T=300\text{K}$.

Figure 2

(Color online) Dispersion of the coupled phonon-plasmon modes ${\omega }_{\pm }$. The red dots with error bars represent our measurements, taken at different primary beam energies $\left(2.5\le E_0\le 80\text{eV}\right)$, the solid blue lines result from theory [Eq. (5)]. The dashed line indicates a $\sqrt{q}$ behavior, which would be typical for a 2DEG. The gap between ${\omega }_{SO}$ and ${\omega }_{\text{TO}}$ is indicated by full horizontal lines (black). The shaded area represents single-particle intraband excitations (Ref. 16) $\left(SP{E}_{intra}\right)$.

Figure 3

(Color online) HREELS spectrum (open circles) taken at 20 eV primary beam energy together with simulation (red solid line). The inset gives details of the two-layer model, $T=130\text{K}$.