Role of Dispersion Forces in the Structure of Graphene Monolayers on Ru Surfaces

Abstract

Elaborate density functional theory (DFT) calculations that include the effect of van der Waals (vdW) interactions have been carried out for graphene epitaxially grown on Ru(0001). The calculations predict a reduction of structural corrugation in the observed moiré pattern of about 25% ($ 0:4 # A) with respect to DFT calculations without vdW corrections. The simulated STM topographies are close to the experimental ones in a wide range of bias voltage around the Fermi level. DOI: 10.1103/PhysRevLett.106.186102 PACS numbers: 73.22.Pr, 68.37.Ef, 68.55.Àa, 71.15.Mb The exceptional electronic properties of perfect twodimensional graphene, such as its high electron mobility or its anomalous quantum Hall effect [1], makes it a promising material for applications in microelectronics and sensing. In practice, synthesis of graphene can be achieved by epitaxial growth of carbon monolayers on transition metals [2][3][4][5]. This has stimulated a lot of experimental work on different metal substrates [4,[6][7][8][9][10][11][12][13][14], which has already led to the production of relatively large domains (a crucial aspect to reproduce the properties of infinitely planar graphene). Nevertheless, in most cases, the presence of the substrate leads to modifications of the graphene morphology. One of these is the appearance of moiré patterns [3], as it is the case for graphene grown on Ru(0001) (G=Ru for short). The presence of moiré patterns not only implies changes in the graphene morphology but also in its electron density, which is no longer uniform [4]. This non uniform electron density is responsible for, e.g., the formation of quantum dots [15,16] or the selective deposition of organic molecules on well defined regions of the graphene sheet [17,18].In spite of the efforts to determine the structural corrugation of the moiré observed in G=Ru, the actual value of such corrugation is still a subject of controversy. Low energy electron diffraction (LEED) experiments give a corrugation of 1.5 Å [19], while surface x-ray diffraction (SXRD) measurements suggest two possible values, 0.82 and 1.5 Å [6,20]. In scanning tunneling microscopy (STM) measurements, the apparent corrugation of the moiré ripples decreases from 1.1 to 0.5 Å when the tunneling bias voltage goes from À0:8 V to þ0:8 V [21]. Helium atom scattering (HAS) experiments, that are sensitive to the surface total charge corrugation, give 0.15-0.4 Å [22]. On the theoretical side, density functional theory (DFT) calculations [19,[23][24][25][26], in which the C and Ru high symmetry directions are aligned but the unit cell is large enough to account for the moiré pattern, predict a corrugation in the range $1:5-1:7 # A [23-25]. In the latter calculations, the effect of van der Waals (vdW) or dispersion forces could not be included. However, there is strong evidence that these forces play a crucial role in the adsorption of aromatic molecules on metal surfaces [27][28][29][30][31], leading, in comparison with nonvdW DFT calculations, to a significant increase of adsorpti...

Exploring the bonding of large hydrocarbons on noble metals: Diindoperylene on Cu(111), Ag(111), and Au(111)

“…Integration of the vdW energy for a single atom adsorbed on a semi-infinite surface yields the atom-surface vdW energy as 38,39 C A-S 3 (z − z 0 ) −3 , where now C A-S coefficient can be determined simply from the C aa 6 and the C bb 6 coefficients that correspond to the adsorbed atom and the metal atom, respectively. However, the situation for real surfaces is more complex because both localized and bulk metal electrons contribute to the C A-S 3 coefficient in a nontrivial 3 . This clearly illustrates that the vdW interaction between an atom and a solid surface is significantly modified by the collective electronic response within the substrate surface.…”

“…During recent years, huge efforts have been made to incorporate vdW interactions into density functional theory (DFT) calculations in order to determine the structure and stability of π -conjugated organic molecules on solid surfaces. [1][2][3][4][5][6] Understanding these interface properties is relevant, inter alia, for electron transfer processes in organic devices. Until now and despite the obvious benefit, there are only a few studies of metal-organic interfaces combining theory and experiment.…”

Probing interlayer interactions between graphene and metal substrates by supersonic rare-gas atom scattering

“…Core-level photoemission has also shown nearly unaltered C1s spectra [11], suggesting that the graphene is indeed nearly freestanding on the Pt(111) substrate. In contrast, gr/Ru(0001) has a huge corrugation on the surface (a moiré corrugation), reflecting a lateral mismatch in the interlayer interaction [22][23][24][25][26][27][28][29][30][31][32][33].…”

Structural and electronic properties of the Ptn–PAH complex (n = 1, 2) from density functional calculations

“…Density functional theory (DFT) has become an invaluable tool in studying the interaction between metal clusters and graphene at the atomic level [9][10][11][12][13][14][15] . However, when considering this type of interaction, the effect of dispersion forces becomes important, as for example in the adsorption of aromatic molecules on metal surfaces [41][42][43][44][45][46][47] . The standard generalized gradient approximation (GGA) functionals, such as the Perdew-BurkeErnzerhof (PBE) 48 functional, do not describe this effect, since it cannot describe electron correlation in situations where the electronic densities of the molecule and surface in practice do not overlap and the dispersion interaction become dominant 41,49 .…”