Quasi-freestanding graphene on Ni(111) by Cs intercalation

A possible approach to achieve quasi-freestanding graphene on a substrate for technological purpose is the intercalation of alkali metal atoms. Cs intercalation between graphene and Ni(111) therefore is investigated using density functional theory, incorporating van der Waals corrections. It is known that direct contact between graphene and Ni(111) perturbs the Dirac states. We find that Cs intercalation restores the linear dispersion characteristic of Dirac fermions, which agrees with experiments, but the Dirac cone is shifted to lower energy, i.e., the graphene sheet is n-doped. Cs intercalation therefore decouples the graphene sheet from the substrate except for a charge transfer. On the other hand, the spin polarization of Ni(111) does not extend through the intercalated atoms to the graphene sheet, for which we find virtually spin-degeneracy.

cases and Table 1 summarizes key findings. In agreement with previous studies 24 , the fcc configuration turns out to have the lowest formation energy  where E Ni is the total energy per atom in bulk Ni and E C is the total energy per C atom in graphene. The fact that the bridge configuration is only 10 meV higher in energy than the fcc configuration implies that it is accessible as well. Even the hcp configuration might be accessible with low probability. Indeed, these configurations experimentally can coexist 25,26 . The hollow configuration, on the other hand, is rather unlikely to be formed.
The C-C bond length in the fcc configuration is 1.44 Å, whereas it is 1.42 Å in pristine graphene. This small tensile strain corresponds to the mentioned small lattice mismatch. The obtained perpendicular distance between graphene and the Ni(111) surface, d C/Ni , see Table 1, is in very close agreement with previous experimental 27 and theoretical 28 findings. For the fcc configuration, Fig. 2 shows the band structure for the spin up and down channels. The Dirac cone is strongly perturbed with a 0.3 eV splitting at the K point, reflecting a strong hybridization between the C 2p and Ni 3d states as a consequence of the small d C/Ni . We obtain finite though small magnetic  We next consider a 2 × 2 supercell with graphene artificially placed in a distance of 6 Å from the Ni(111) substrate, see Fig. 3(c). As expected, this distance yields a weak interaction between the Ni 3d and C 2p states, compare the almost vanishing Ni-C hybridization, leading to a restoration of the Dirac cone with a minor splitting. In fact, hybridization effects start vanishing in distances larger than 3 Å. Figure 3(a,b) shows the band structures of the spin up and down channels. We obtain a shift of the Dirac point by 0.2 eV above the Fermi level, reflecting p-doped graphene. The Dirac cone appears in the two spin channels at the same energy, implying that there is no C magnetic moment. The Ni bands, on the other hand, show a rigid shift due to spin polarization. Projected densities of states in Fig. 3(c) confirm that the magnetic moments on the C atoms are zero and that the total magnetic moment of 10.8 μ B comes from the Ni atoms, where atoms in the first layer show magnetic moments of 0.67 μ B and atoms in the other layers show 0.68 μ B .
We find that intercalation of Cs enlarges the distance between the graphene sheet and the Ni(111) substrate to 6.0 Å post relaxation (3.1 Å from graphene to Cs and 2.9 Å from Cs to Ni). The in-plane Cs-Cs distance is 5.0 Å. We note that the graphene sheet shows no significant structural modification, see Fig. 4(c), in particular hardly any buckling. According to Fig. 4(a,b), the electronic structure, on the other hand, is altered substantially by the Cs intercalation. In particular, a multitude of bands appears from − 1.5 to 0.5 eV. To understand the origin of these bands we use a weighted band analysis. Figure 5(a) shows that the cone-like bands originate from the C 2p states, while the other bands are due to the Ni 3d states. The Dirac cone is restored with a negligible splitting. It appears about 1.1 eV below the Fermi level, representing prominently n-doped graphene. The C atoms carry no magnetic moment, see also Fig. 4(d), implying that Cs does not transfer spin polarization from Ni to graphene. In the Ni(111) substrate the magnetic moments decrease towards Cs from a value of 0.68 μ B , which is close to the bulk Ni value of 0.67 μ B , to values of 0.49 μ B for the atom directly below Cs and 0.59 μ B for the other atoms in the same layer.
We next consider larger supercells, see Fig. 5 on top, to study the effect of the Cs concentration. The weighted band structures obtained for 2 × 2 (without and with intercalation), 3 × 3, and 4 × 4 supercells in Fig. 5 demonstrate a shift of the Dirac point upwards to the Fermi level when the Cs concentration is reduced. The higher the Cs concentration the stronger is the n-doping of graphene. The Dirac point is located 1.12 eV, 0.61 eV, and 0.59 eV below the Fermi level, respectively, for the 2 × 2, 3 × 3, and 4 × 4 supercell, which corresponds to a charge transfer of 0.045, 0.012, and 0.011 electrons in the case of pristine graphene.
As another ferromagnetic substrate we have also considered Co(0001) to check whether our results for Ni(111) are of general validity. The band structure of the 2 × 2 supercell, see Fig. 6(a,b), is found to show close similarity to the case of the Ni(111) substrate, only the Dirac point is shifted slightly more (1.17 eV) below the Fermi level. The projected densities of states in Fig. 6(c), on the other hand, indicate that Co is subject to a stronger exchange splitting as compared to Ni.

Discussion
We have investigated the effect of Cs intercalation on the structural, electronic, and magnetic properties of graphene on Ni(111) and Co(0001). An fcc configuration is found to be energetically favorable in agreement with previous experimental and theoretical results, and therefore is chosen for studying the intercalation. Different supercell sizes have been considered to examine the effect of the Cs concentration. In agreement with experimental results, the Cs intercalation restores the Dirac cone, since it decouples graphene from the substrate, resulting in n-doped quasi-freestanding graphene. Both for the Ni(111) and Co(0001) substrates the graphene sheet exhibits no trace of spin polarization.

Methods
Density functional theory is employed using the Vienna Ab-initio Simulation Package 30 and the generalized gradient approximation (Perdew-Burke-Ernzerhof parametrization 31 ) along with ultrasoft pseudopotentials. London forces are considered in all calculations 32 and the plane wave cutoff energy is set to 500 eV. Supercells are created using in the xy-plane the lattice parameter of Ni (2.49 Å) and adding a vacuum slab of about 15 Å thickness in the z-direction. For a 1 × 1 unit cell of graphene on Ni(111) a 32 × 32 × 1 k-mesh (Monkhorst-Pack scheme 33 ) is used for the Brillouin zone integration (16 × 16 × 1 for the structure relaxation). We built a 2 × 2 supercell containing 24 atoms (8 C and 16 Ni) and introduce one Cs atom, giving a total number of 25 atoms. Also 3 × 3 and 4 × 4 supercells are constructed to examine the effect of the Cs concentration. These supercells are relaxed using 4 × 4 × 1 and 2 × 2 × 1 k-meshes, respectively, and 8 × 8 × 1 and 4 × 4 × 1 k-meshes are employed for the self-consistency calculation.