High-energy collective electronic excitations in free-standing single-layer graphene

In this joint experimental and theoretical work, we investigate collective electronic excitations (plasmons) in free-standing, single-layer graphene. The energy- and momentum-dependent electron energy-loss function was measured up to $50\phantom{\rule{0.28em}{0ex}}\mathrm{eV}$ along two independent in-plane symmetry directions ($\ensuremath{\Gamma}M$ and $\ensuremath{\Gamma}K$) over the first Brillouin zone by momentum-resolved electron energy-loss spectroscopy in a transmission electron microscope. We compare our experimental results with corresponding time-dependent density-functional theory calculations. For finite momentum transfers, good agreement with experiments is found if crystal local-field effects are taken into account. In the limit of small and vanishing momentum transfers, we discuss differences between calculations and the experimentally obtained electron energy-loss functions of graphene due to a finite momentum resolution and out-of-plane excitations.