Graphene on Ir(111): Physisorption with Chemical Modulation

The nonlocal van der Waals density functional approach is applied to calculate the binding of graphene to Ir(111). The precise agreement of the calculated mean height $\overline{h}=3.41\AA$ of the C atoms with their mean height $\overline{h}=(3.38\pm 0.04)\AA$ as measured by the x-ray standing wave technique provides a benchmark for the applicability of the nonlocal functional. We find bonding of graphene to Ir(111) to be due to the van der Waals interaction with an antibonding average contribution from chemical interaction. Despite its globally repulsive character, in certain areas of the large graphene moiré unit cell charge accumulation between Ir substrate and graphene C atoms is observed, signaling a weak covalent bond formation.

Figure 1

(a) Squares: X-ray photoelectron spectroscopy (XPS) intensity of the C $1s$ peak for 0.63 ML of graphene on Ir(111). Thin line:  Shirley-type background; thick line: Gaussian fit (full width at half maximum 0.85 eV) above background. (b) X-ray reflectivity (triangles) normalized using the fit to the data (solid line [37]) and exemplary C $1s$ photoemission yield normalized to an off-Bragg yield of 1 (squares: 0.39 ML, circles: 0.63 ML, shifted upwards by unit of 1 for easier readability). Solid lines: Fits to the data [23, 37] taking into account additional broadening due to the mosaicity of the sample and the bandpass of the x-ray beam.

Figure 2

(a) Top view and (b) side view [cut along the dashed line in (a)] of the relaxed structure of graphene/Ir(111) obtained by DFT including vdW interactions. Regions of high-symmetry stacking (fcc, hcp, top) are marked by circles (a) or arrows (b)–(d). The color scale in (b) and (a) ranges from $h=3.20\AA$ (dark) to $h=3.65\AA$ [light gray (yellow)]. (c) Visualization of the nonlocal-correlation binding-energy density $e_c^{\mathrm{nl},\mathrm{bind}}(\mathbf{r})$ caused by adsorption. The color scale ranges from $e_c^{\mathrm{nl},\mathrm{bind}}(\mathbf{r})=0\mathrm{meV}{\AA }^{-3}$ [dark gray (blue)] over light gray (green) to $e_c^{\mathrm{nl},\mathrm{bind}}(\mathbf{r})=-28.3\mathrm{meV}{\AA }^{-3}$ [medium gray (red)]. (d) Charge transfer upon adsorption. The color scale ranges from $\Delta \rho =-0.0138e{\AA }^{-3}$ [dark gray (blue)] over light gray (green) to $\Delta \rho =0.013e{\AA }^{-3}$ [medium gray (red)]. A negative value indicates loss of electron density. (e) Magnified view of red box in (d). Views from different angles can be obtained in [25].

Figure 3

STM topographs of graphene on Ir(111). (a) 0.39 ML. Flakes with the characteristic graphene moiré are visible. (b) 0.63 ML. A sheet extends over a wide area including a substrate step. Lowest regions are bare Ir(111). Image widths 1000 Å, bias voltage $U_{\mathrm{sample}}=-1\mathrm{V}$, tunneling current $I=0.2\mathrm{nA}$ (a), $I=0.06\mathrm{nA}$ (b).