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 $ensuremath{pi}$ and $ensuremath{pi}+ensuremath{sigma}$-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 $ensuremath{pi}$- and $ensuremath{pi}+ensuremath{sigma}$ 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.