Graphene on Ru(0001): The four hills in the 25 on 23 structure

A single layer of sp2 hybridized carbon on Ru(0001) accommodates in a 23 on 25 superstructure with 625 carbon honeycombs as found by surface x-ray diffraction (SXRD) [1]. In a significant computational effort 25x25 unit cells of graphene were relaxed on 23x23 Ru(0001) unit cells with up to 6 substrate layers. The density functional theory calculations that take van der Waals interactions into account predict 4 protrusions, quantum dots [2] or ``hills'' in the unit cell with two kinds of hills: 3 $\Omega$-type hills with a honeycomb around the summits, and one T-type hill with a single carbon atom on the summit. This prediction is confirmed by state of the art low temperature scanning tunneling microscopy and is in line with the SXRD data in Ref.[1].\\[4pt] [1] Martoccia et al. Phys. Rev. Lett. 101 (2008) 126102.\\[0pt] [2] Zhang et al. J. Phys.: Condens. Matter 22 (2010) 302001.