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 $3.40–3.72\text{Å}$. 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.

Figure 1

(Color online) Binding energy $\left(E_b\right)$ per carbon atom of graphene on the Ni(111) surface calculated with LDA, revPBE, and vdW-DF functionals. The graphene is adsorbed in the top-fcc configuration (see inset).

Figure 2

LDA (top) and vdW-DF (bottom) band structures for graphene on Ni(111) in the top-fcc configuration. Larger dots represent larger weight of the carbon $p_z$ orbitals. Only one spin channel is shown, the other being almost identical.

Figure 3

(Color online) Decomposition of the binding energy $E_b$ into exchange-only contributions (dashed lines—only the correlation term is removed) and total binding energy (full lines) for different functionals.