Density functional study of the Au-intercalated graphene/Ni(111) surface

We have studied the effect of Au intercalation on the atomic and electronic structure of the graphene/Ni(111) surface by using density functional theory calculations. Our calculations demonstrate that (1) Au atoms energetically favor interface intercalation over surface adsorption, (2) Au intercalation drastically changes the electronic structure of graphene/Ni(111) so that the graphene $\pi$ bands almost recover the Dirac cone of ideal free-standing graphene, and (3) the Fermi edge locates closely at the Dirac point, indicating that the underlying Au/Ni(111) substrate is inert. The present theory confirms a recent experimental claim that graphene grown on Ni(111) and intercalated by one monolayer Au can be regarded as quasifree standing.

Figure 1

(Color online) Atomic and electronic structure of the graphene/Ni(111) surface. (a) Equilibrium geometry. Large and small balls represent the Ni and C atoms, respectively. Dashed lines represent a $\left(2\times 2\right)$ unit cell with three high-symmetry surface sites denoted by crosses. C atoms are all above the top and fcc hollow sites. The $\left(2\times 2\right)$ surface Brillouin zone is shown. (b) Band structure of majority-spin states. Open (filled) circles represent the C-derived (Ni-derived) surface states which contain more than 25% (35%) of charge in the graphene (topmost Ni) layer. Solid lines represent the bands of free-standing graphene, given as a reference. The Fermi energy is set to zero.

Figure 2

(Color online) Structural model for the graphene/Au/Ni(111) surface. Large, medium, and small balls represent Ni, Au, and C atoms, respectively. Here, the sizes of atoms are not proportional to their atomic radii but chosen for a better presentation of the geometry. Dashed lines represent a $\left(2\times 2\right)$ unit cell. Au atoms occupy the top, fcc, and hcp sites of Ni(111), and the Au coverage corresponds to 0.75 ML. C atoms are above the top and fcc sites of Ni(111).

Figure 3

(Color online) Band structures of (a) graphene/Au/Ni(111) and (b) graphene/Au. In (a), the bands of majority-spin states are shown. In (b), the bands are spin unpolarized and the underlying structure represents the frozen graphene/Au/Ni(111) surface with the Ni(111) substrate removed. Large, medium, and small open circles represent C-derived surface states which contain more than 75%, 50%, and 25% of charge in graphene, respectively. Gray (black) filled circles represent Ni-derived (Au-derived) surface states which contain more than 35% of charge in the topmost Ni (Au) layer. Solid lines represent the bands of free-standing graphene.

Figure 4

(Color online) Band gap $\left(E_{\text{g}}\right)$ and Dirac point $\left(E_{\text{D}}\right)$ relative to $E_{\text{F}}$ in the graphene $\pi$ bands as a function of the Au coverage. Here, the Dirac point is defined as the midpoint of the band gap. All data were given for the majority-spin band structure.

Figure 5

(Color online) Simulated constant-current STM images: (a) graphene/Ni(111), (b) graphene/Au/Ni(111), and (c) free-standing graphene. The filled-state images were obtained by integrating $\rho \left(r,E\right)$ from $E_{\text{F}}-2.0\text{eV}$ to $E_{\text{F}}$, and the empty-state images from $E_{\text{F}}$ to $E_{\text{F}}+2.0\text{eV}$. The images represent the surface of constant density with $\rho =1\times {10}^{-3}e/{\text{Å}}^3$.