Electron localization in epitaxial graphene on Ru(0001) determined by moire corrugation

The interpretation of scanning tunneling spectroscopy (STS) and scanning tunneling microscopy measurements of epitaxial graphene on lattice-mismatched substrates is a challenging problem, because of the spatial modulation in the electronic structure imposed by the formation of a moire pattern. Here we describe the electronic structure of graphene adsorbed on Ru(0001) by means of density functional theory calculations that include van der Waals interactions and are performed on a large 11 x 11 unit cell to account for the observed moire patterns. Our results show the existence of localized electronic states in the high and low areas of the moire at energies close to and well above the Fermi level, respectively. Localization is due to the spatial modulation of the graphene-Ru(0001) interaction and is at the origin of the various peaks observed in STS spectra.