We have performed low temperature scanning tunnelling spectroscopy (STS) measurements on graphene epitaxially grown on Ru(0001). An inelastic feature, related to the excitation of a vibrational breathing mode of the graphene lattice, was found at 360 meV. The change in the differential electrical conductance produced by this inelastic feature, which is associated with the electron-phonon interaction strength, varies spatially from one position to other of the graphene supercell. This inhomogeneity in the electronic properties of graphene on Ru(0001) results from local variations of the carbon-ruthenium interaction due to the lattice mismatch between the graphene and the Ru(0001) lattices.
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