International audienceIn 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 50eV along two independent in-plane symmetry directions (ΓM and ΓK) 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

PACS 78.67.-n-Optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures PACS 78.67.Wj-Optical properties of graphene PACS 73.20.Mf-Collective excitations (including excitons, polarons, plasmons and other charge-density excitations) Abstract-In low-dimensional systems, a detailed understanding of plasmons and their dispersion relation is crucial for applying their optical response in the field of plasmonics. Electron energyloss spectroscopy is a direct probe of these excitations. Here we report on electron energy-loss spectroscopy results on the dispersion of the π plasmons in free-standing graphene monolayers at the momentum range of 0 |q| 0.5Å −1 and parallel to the Γ-M direction of the graphene Brillouin zone. In contrast to the parabolic dispersion in graphite and in good agreement with theoretical predictions of a 2D electron gas of Dirac electrons, linear π plasmon dispersion is observed. As with previous EELS results obtained from single-wall carbon nanotubes, this can be explained by local-field effects in the anisotropic 2D system yielding a significant contribution of the low-energy band structure on the high-energy π plasmon response.

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High-energy collective electronic excitations (plasmons) in freestanding multilayer graphene are studied by momentum-resolved electron energy-loss spectroscopy (EELS). For normal incidence, only the high-energy plasmon band is excited and we measure a blueshift of the π-plasmon dispersion with increasing thickness. The observed transition between two-dimensional and three-dimensional behavior is explained using a layeredelectron-gas (LEG) model. We propose a method to measure all individual plasmon bands by tilting the sample with respect to the electron beam. As a proof of concept, EELS experiments for three-layer graphene are compared with predictions from the LEG model.

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