Lattice-matched versus lattice-mismatched models to describe epitaxial monolayer graphene on Ru(0001)

Monolayer graphene grown on Ru(0001) surfaces forms a superstructure with periodic modulations in its geometry and electronic structure. The large dimension and inhomogeneous features of this superstructure make its description and subsequent analysis a challenge for theoretical modeling based on density functional theory. In this work, we compare two different approaches to describe the same physical properties of this surface, focusing on the geometry and the electronic states confined at the surface. In the more complex approach, the actual moire structure is taken into account by means of large unit cells, whereas in the simplest one, the graphene moire is completely neglected by representing the system as a stretched graphene layer that adapts pseudomorphically to Ru(0001). As shown in previous work, the more complex model provides an accurate description of the existing experimental observations. More interestingly, we show that the simplified stretched models, which are computationally inexpensive, reproduce qualitatively the main features of the surface electronic structure. They also provide a simple and comprehensive picture of the observed electronic structure, thus making them particularly useful for the analysis of these and maybe other complex interfaces.