First principles study of the graphene/Ru(0001) interface.

Annealing the Ru metal that typically contains residual carbon impurities offers a facile way to grow graphene on Ru(0001) at the macroscopic scale. Two superstructures of the graphene/Ru(0001) interface with periodicities of 3.0 and 2.7 nm, respectively, were previously observed by scanning tunneling microscopy. Using first principles density functional theory, we optimized the observed superstructures and found interfacial C-Ru bonding of C atoms atop Ru atoms for both superstructures, which causes the graphene sheet to buckle and form periodic humps of approximately 1.7 A in height within the graphene sheet. The flat region of the graphene sheet, which is 2.2-2.3 A above the top Ru layer and has more C atoms occupying the atop sites, interacts more strongly with the substrate than does the hump region. We found that interfacial adhesion is much stronger for the 3.0 nm superstructure than for the 2.7 nm superstructure, suggesting that the former is the thermodynamically more stable phase. We explained the 3.0 nm superstructure's stability in terms of the interplay between C-Ru bonding and lattice matching.