Plasmon spectroscopy of free-standing graphene films

Plasmon spectroscopy of the thinnest possible membrane, a single layer of carbon atoms: graphene, has been carried out in conjunction with ab initio calculations of the low loss function. We observe $\pi$ and $\pi +\sigma$-surface plasmon modes in free-standing single sheets at 4.7 and 14.6 eV, which are substantially redshifted from their values in graphite. These modes are in very good agreement with the theoretical spectra, which find the $\pi$- and $\pi +\sigma$ in-plane modes of graphene at 4.8 and 14.5 eV. We also find that there is little loss caused by out-of-plane modes for energies less than about 10 eV.

Figure 1

(Color online) (a)–(c) HAADF STEM images of ‘clean’ patches revealing one, two, and five layers of graphene. The area in the white-framed boxes has been subjected to a low pass filter to disclose the atoms more clearly: In the single layer the atoms in the six rings are white and the hexagon center is black. (d) Intensity traces have been taken along the long dimensions of the rectangular cyan-framed boxes in (a)–(c); these traces were then averaged over 40 pixels (width of boxes). They show step-wise increase of the HAADF intensity corresponding to the layer number. The vacuum intensity is at $\sim 268$. (e) EEL spectra of one, two, five and several layers of graphene showing the $\pi$-and the $\pi +\sigma$ plasmon. The spectra are extracted from spectrum images; they are background subtracted and each summed over 25 pixels.

Figure 2

(Color online) The loss function for graphite with a separation between $c$-planes equal to 20 and 10 times its separation in graphite and for graphite itself. Figure 2 (top) is case where $\mathit{q}\parallel \mathit{c}$ and Fig. 2 (bottom) when $\mathit{q}\parallel \mathit{a}$. $Y$ axis: arbitrary units, $x$ axis: energy loss in eV.

Figure 3

(Color online) Comparison of the loss function for a single and multilayers of graphene for $\mathit{q}\parallel \mathit{c}$ (top) and $\mathit{q}\parallel \mathit{a}$ (bottom). Note, the loss around 4 eV in the $\mathit{q}\parallel \mathit{c}$ case for the multilayer case and its absence for single layer graphene (shown as red line). Note also the increasing redshift of the main peaks above about 10 eV as the number of layers decreases. $Y$ axis: arbitrary units, $x$ axis: energy loss in eV.