Figure 1

(a) STM image ($150\times 150{\AA }^2$, $V_s=-0.5\mathrm{V}$) measured at 4.6 K at the edge of a graphene island. The left-hand side is the uncovered Ru(0001) surface, while on the right-hand side the moiré superlattice of graphene appears as a triangular array of bumps. (b) $dZ/dV$ curves measured on the moiré superstructure on the graphene island. The blue (dark gray) curve was measured in the $H$ areas [blue (dark gray) box in (a)]. The red (medium gray) curve shows the corresponding spectra measured in the $L$ areas of the moiré [red (medium gray) box in (a)]. Inset in (b) shows $dZ/dV$ curve measured on the clean Ru(0001) [green (light gray) box in (a)].Reuse & Permissions

Figure 2

(a) STM topographic image ($90\times 90{\AA }^2$, $V_s=-0.5\mathrm{V}$) measured simultaneously with the $dZ/dV$ maps shown in the other panels. (b) $dZ/dV$ map showing the spatial distribution of the new feature that appears at $+3\mathrm{V}$ in the $L$ areas of the moiré superstructure. (c) $dZ/dV$ map showing the spatial distribution of the feature that appears in the spectra a $+4.4\mathrm{V}$. The intensity of this feature is strictly confined to the $H$ areas of the moiré. (d) $dZ/dV$ map showing that the feature that appears in the spectra a $+4.8\mathrm{V}$ is confined to the $L$ areas of the moiré. The red circle marks the same spot in all the images.Reuse & Permissions

Figure 3

The calculated evolution of the energies (relative to the Fermi level) of the unoccupied states at $\Gamma$, i.e., within the projected band gap of Ru(0001), when a laterally strained graphene layer is approached to the surface. The green horizontal lines, at the right-hand side, show the energy position of the states for a freestanding strained graphene layer with our basis set of numerical orbitals supplemented with diffuse orbitals. States labeled with $1^{+}$ and $1^{-}$ correspond to the first and second image states [13]. The letters refer to the different panels of Fig. 4. Squares and circles indicate the doubly and singly degenerate states.Reuse & Permissions

Figure 4

Planar average of the density associated with selected states in our DFT calculations of strained graphene on Ru(0001). The dashed black line marks the Ru(0001) surface and the continuous red line the graphene plane. The letters of the panels correspond to the letters shown in Fig. 3. For a graphene-Ru distance $d=3\AA$, relatively weak C-Ru interaction ($H$ areas), the Ru surface resonance remains unchanged (e) while the first FER corresponds to the $1^{+}$ image state modified by the neighboring Ru (f). At $d=2.4\AA$ ($L$ areas), stronger interaction, the interfacial state displaces its charge appreciably outside the graphene layer due to the interlayer confinement (c), while the first FER has its charge distributed on both sides of the $C$ surface (d). A further pushing of the C layer towards the metal to $d=2\AA$ reveals an avoided crossing of the two bands by the exchange in character of the states [(a) and (b)].Reuse & Permissions