Graphene on Ru(0001) Moiré Corrugation Studied by Scanning Tunneling Microscopy on Au/Graphene/Ru(0001) Heterostructures

Two-dimensional Au islands of different thicknesses grown on graphene/Ru(0001) were used to study the corrugation of the moiré structure of graphene/Ru(0001) and discriminate between its mainly structural or electronic character. A comparison of the apparent corrugation measured by scanning tunneling microscopy (STM) for different Au thicknesses with results of elasticity theory equations applied to a gold film over a corrugated substrate shows that the corrugation observed for the graphene/Ru(0001) moiré is of structural nature rather than electronic. STM showed a large value for the corrugation of the first Au monolayer on graphene/Ru(0001), 1.7 Å; using density functional theory calculations, we explain this large corrugation of the Au monolayer as the result of a strong (weak) binding of the Au layer at the valley (hill) regions of the graphene/Ru(0001) moiré structure and infer an actual corrugation of the graphene/Ru(0001) moiré structure of ∼1.2 Å from the measured corrugation of the Au monolayer.