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Many of the peculiar properties of graphene are related to its collective excitations, even if their understanding is still lacking. Plasmons are collective longitudinal modes of charge fluctuation in metal samples excited by an external electric field. Plasmons find applications in magneto-optic data storage, optics, microscopy, and catalysis. Plasmons in graphene have unusual properties and offer promising prospects for plasmonic applications covering a wide frequency range, going from terahertz up to the visible. On the other hand, lattice dynamics play an important role in many chemical and physical processes. The investigation of phonons in materials provides information on numerous properties, such as sound velocity, thermal expansion, magnetic forces, heat capacity, and thermal conductivity. High-resolution electron energy loss spectroscopy is the main experimental technique for investigating collective excitations (both plasmons and phonons), with adequate resolution in both the energy and momentum domains to investigate surface electronic excitations. This chapter discusses the status and the prospect of research on collective excitations (plasmons and phonons) in graphene epitaxially grown on metals.
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