Graphene on metals: A van der Waals density functional study

We use density functional theory (DFT) with a recently developed van der Waals density functional (vdW-DF) to study the adsorption of graphene on Co, Ni, Pd, Ag, Au, Cu, Pt, and Al(111) surfaces. In contrast to the local-density approximation (LDA) which predicts relatively strong binding for Ni,Co, and Pd, the vdW-DF predicts weak binding for all metals and metal-graphene distances in the range $3.40--3.72\text{ }\text{\AA{}}$. At these distances the graphene band structure as calculated with DFT and the many-body ${G}_{0}{W}_{0}$ method is basically unaffected by the substrate, in particular there is no opening of a band gap at the $K$ point.