SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION Method: Epitaxial graphene was prepared by heating an Ir(111) crystal to 550 K for 100 s under 2 x 10-5 Pa partial pressure of ethylene, followed by a flash anneal to 1420 K 1. This cycle was repeated seven times in order to obtain a high-quality graphene layer and to achieve complete surface coverage. The quality of the graphene layer was confirmed by STM, ARPES and Low-Energy Electron Diffraction. Atomic hydrogen was deposited onto the graphene layer at room temperature by means of a 2100 K hot H-atom beam with a flux of ~ atoms/cm 2 s. STM images where obtained by the Aarhus STM 2 with the sample held at room temperature. ARPES data were recorded on the SGM-3 beamline at ASTRID synchrotron at the Institute for Storage Ring Facilities at Aarhus University 3. The sample was kept at 100K while collecting the data sets. Determination of possible gap openings around the K point involve the potential risk of error due to small sample misalignments. To ensure that this is not the case, ARPES data sets were actually not taken as twodimensional cuts in k-space as in Fig. 1 but as three dimensional maps with the photoemission intensity measured as a function of binding energy and a twodimensional k-vector parallel to the surface. The scans in Fig. 1 have been extracted from such data sets. Figs. S1a and S1b show alternative cuts of the same data sets, taken as a function of k at constant binding energies of 50 mev, 500 mev and 800 mev, for clean graphene, and after a 50 s hydrogen exposure The cut through the Dirac cone at higher binding energy shows the typical anisotropic intensity distribution, which is a consequence of constructive and destructive interference between the electron wave functions associated with the two sub-lattices in graphene 4. nature materials 1

2 From the evolution of these contours, one can determine the location of the Dirac point precisely and accordingly the lines in the topmost images in Fig. S1 mark the positions at which the dispersion planes for Fig. 1 were obtained. The distinct difference in size of the horseshoe contour at fixed binding energy in Figs. S1a and S1b and the fact that horseshoe approaches the small circle near the Fermi level and 500 mev for the clean and hydrogenated graphene surface, respectively, clearly point towards a hydrogen-induced gap opening. In Fig. S1b the iridium bands also become evident as the graphene π-band signal becomes fairly weak. Density functional theory calculations of adsorption structures of H atoms on graphene on Ir(111) were performed with the DACAPO computer code 5, applying ultra-soft pseudopotentials 6,7 to describe electron-ion interactions, and the Perdew Wang functional 8 (PW91) for the electronic exchange correlation effects. The electron wave functions and augmented electron density were expanded in plane waves with cut-off energies of 25 Ry and 140 Ry, respectively. Sampling of the Brillouin zone was restricted to the Γ-point. The graphene layer, as well as the Ir(111) surface are modelled using supercell slab geometry. Due to the computational limitations, experimentally observed graphene moiré pattern on the Ir(111) surface is modelled as a 8x8 graphene sheet on a 7x7 Ir(111) layer. The in-plane distances between Ir atoms are expanded by ~3% to match periodicity of the graphene pattern. The graphene binding to the metal support calculated by modelling the Ir(111) surface with a single layer is obviously overestimated. However, our test calculations demonstrate that the site preference for the binding of H clusters on the graphene supported by a single Ir(111) layer, is not altered when additional Ir atoms are placed in the second and third fcc(111) layer. 2 nature MATERIALS

3 Density Functional-based Tight-Binding (DFTB, for a detailed description see ref. 9) calculations were performed with a bare and hydrogenated graphene layer. To emulate the effect of the Ir substrate, the supercell lattice constant of Å was used, i.e. 10 times the graphene lattice constant a = 2.46 Å, very similar to the moiré periodicity of 25 Å observed for graphene on Ir(111). DFTB is known to produce reliable geometries and energies for hydrocarbons 9 and has recently been applied in the study of H-terminated holes in graphene antidot lattices6. Geometries were relaxed by sampling the energy in the corners and line midpoints of the Γ-M-K wedge. The positions of all atoms within the H-covered regions, including undecorated C atoms at neighbor sites, were relaxed. After relaxation, residual average forces were below 0.05 ev/å. It is evident that the actual samples are far more disordered than the idealized geometries considered in Fig. 4. Disorder manifests itself in two separate ways: (i) Different H coverages are found for different moiré supercells and (ii) within each supercell, H atoms adsorb in partly disordered non-symmetric patterns. To simulate the effects on the electronic structure, we have generated partly disordered geometries by random removal of H atoms from the top side of a graphane-like island geometry ( c.f. Fig. 4). H-coverage in the ideal structure is 42% corresponding to 42 H atoms on the top side. We removed 4, 8 or 16 of these from random sites and allowed the unpaired C atom to relax (force threshold 0.25 ev/å). Furthermore, dissimilarity between moiré cells was studied by averaging over 10 such disordered geometries. The density of states (DOS) based on this procedure is illustrated in Fig. S2a. Several trends with increased disorder are noticed. First, the valence band edge shifts to lower energies and develops a tail into the ideal gap. Second, the conduction band DOS is fragmented into an irregular structure stretching into the gap and the fragmentation nature materials 3

4 increases with disorder. These disorder-induced gap states are spatially localized as demonstrated by the flat bands in Fig. S2b. Such localized gap states are expected to produce a diffuse background in the ARUPS spectra. Also, the valence band tail will increase the width of the valence band structure. These observations are in good agreement with the observed trend in Fig nature MATERIALS

5 References 1 Coraux, J. et al. Growth of graphene on Ir(111). New J, Phys. 11, (2009). 2 Laegsgaard, E., Besenbacher, F., Mortensen, K., & Stensgaard, I. A Fully Automated, Thimble-Size Scanning Tunneling Microscope. J. Microsc-Oxford 152, (1988). 3 Hoffmann, S.V., Sondergaard, C., Schultz, C., Li, Z., & Hofmann, P. An undulator-based spherical grating monochromator beamline for angle-resolved photoemission spectroscopy. Nucl. Instrum. Meth. A 523, (2004). 4 Mucha-Kruczyński, M. et al., Characterization of graphene through anisotropy of constantenergy maps in angle-resolved photoemission. Phys. Rev. B 77, 12 (2008). 5 Hammer, B., Hansen, L., & Norskov, J., Improved adsorption energetics within densityfunctional theory using revised Perdew-Burke-Ernzerhof functionals. Phys. Rev. B 59, (1999). 6 Vanderbilt, D., Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, (1990). 7 Laasonen, K., Pasquarello, A., Car, R., Lee, C., & Vandrbilt, D., Car-Parrinelo moleculardynamics with Vanderbilt ultrasoft pseudopotentials. Phys. Rev. B 47, (1993). 8 Perdew, J. et al., Atoms, molecules, solids and surfaces - applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, (1992). 9 Porezag, D., Frauenheim, T., Kohler, T., Seifert, G., & Kaschner, R. Construction of tightbinding-like potentials on the basis of density-functional theory - application to carbon. Phys. Rev. B 51, (1995). nature materials 5

6 Fig. S1) Photoemission intensity near the K-point at constant binding energies (given at the centre) and as a function of wave vector parallel to the surface. The horseshoe -like intensity distribution is characteristic for photoemission away from the Dirac point. For a given energy, the size of the horseshoe is smaller in b) than in a), indicative of a band gap opening. Additional photoemission features in b) are from the Ir(111) substrate. The lines in the topmost images indicate the cuts chosen for displaying the dispersion in Fig nature MATERIALS

7 Figure S2) Effects of disorder on H-decorated structures exemplified by the graphane-like island (c.f. Fig. 4). Modifications of the density of states (a) and band structure (b) upon removal of random H atoms from the top side are shown. In (a), 4, 8 or 16 H atoms are removed from random sites and the density of states is averaged over 10 such disordered geometries. The band structure in (b) is an example for a particular randomly disordered geometry with 8 H atoms removed. The flat bands are a result of localized gap states induced by disorder. nature materials 7