Comparative van der Waals density-functional study of graphene on metal surfaces

We present a comparative van der Waals density-functional (vdW-DF) study of graphene adsorbed on (111) surfaces of Ni, Cu, Pd, Ag, Au, and Pt, using the second version of vdW-DF (vdW-DF2) of Lee et al. [Phys. Rev. B 82, 081101(R) (2010)] and the exchange functional (C09) developed by Cooper [Phys. Rev. B 81, 161104(R) (2010)]. We show that the use of the vdW-DF2 correlation together with the C09 exchange yields the most satisfactory results: Adsorption geometries of graphene are in good agreement with available experiment data, and the electronic structure of graphene varies depending on the nature of the substrate. Band-gap opening at the $K$ point observed on the Ni(111) surface is reproduced reasonably well.

Figure 1

(Color online) Adsorption geometry of graphene on (a) Ni and Cu and (b) Pd, Ag, Au, and Pt substrates. Small and large balls represent graphite and metal atoms, respectively. Unit cells are indicated by parallelograms. Vertical arrows shown in the lower figure indicate the adsorption distances.

Figure 2

(Color online) Binding energy of graphene with the Ni(111) surface as a function of adsorption distance.

Figure 3

(Color online) Band structure of graphene adsorbed on Ni, Cu, Pd, and Au (111) surfaces, calculated at the equilibrium distances obtained using $\text{vdW-DF}{2}^{\text{C}{09}_x}$. Only the up-spin state is shown for Ni and the down-spin state is similar and not shown. For band structures for other metal substrates, see supplemental material.