Epitaxial graphene monolayer and bilayers on Ru(0001): Ab initio calculations

We studied very large graphene/Ru systems by ab initio calculations. It is shown that the graphene monolayer on Ru is nearly flat rather than strongly corrugated. The large corrugation is found to be unfavorable and disagrees with the observed bias dependence of scanning tunnel microscope images. The C-Ru bonds are metallic instead of covalent. A new moire structure arises between graphene bilayers and the generally supposed Bernal stacking is broken. The second layer has higher density of C atoms and is slightly corrugated. While the electronic states of the first graphene layer are shifted down by about 1 eV, the electronic structure of the second one resembles that of the free graphene, in good agreement with the experiments.