Symmetry Driven Band Gap Engineering in. Hydrogen Functionalized Graphene

Transcription

1 Symmetry Driven Band Gap Engineering in Hydrogen Functionalized Graphene Jakob H. Jørgensen 1, Antonija Grubišić Čabo 1, Richard Balog 1,2, Line Kyhl 1, Michael Groves 1, Andrew Cassidy 1, Albert Bruix 1, Marco Bianchi 1, Maciej Dendzik 1, Mohammad Alif Arman 3, Lutz Lammich 1, José Ignacio Pascual 2, Jan Knudsen 3,4, Bjørk Hammer 1, Philip Hofmann 1, Liv Hornekær 1* 1 Department of Physics and Astronomy and Interdisciplinary Nanoscience Center inano, Aarhus University, DK 8000 Aarhus C, Denmark 2 CIC nanogune and Ikerbasque Basque Foundation of Science, Donostia-San Sebastian 20018, Spain 3 Lund University, Division of Synchrotron Radiation Research, Box 118, Lund, Sweden 4 Lund University, The MAX IV Laboratory, Box 118, Lund, Sweden * liv@phys.au.dk

2 S1: Computational methods Density functional theory (DFT) was employed to atomically model the hydrogen atom adsorption onto graphene over the iridium surface. The real-space, grid based projector augmented wave method GPAW was used 1, 2 in conjunction with the Atomic Simulation Environment (ASE). 3 Experimental results and DFT calculations show that both strong electronic interactions and van der Waals (vdw) bonding exists between the graphene and the substrate. 4 Therefore, the van der Waals enabled functional optb88-vdw 5 was employed to explicitly calculate both parts. The functional uses the vdw-df framework developed by Dion et al. 6 with a version of B88 exchange 7 parameterized to the S22 dataset. 8 optb88-vdw performs well against a broad cross-section of dispersion-enabled functionals including hybrid functionals and the random phase approximation. 9 Furthermore, it accurately calculates the binding energy between benzene and many transition metal surfaces, that is, 10, 11 conjugated systems where vdw effects are very important. The implementation of vdw-df functionals, including optb88-vdw, uses a fast- Fourier transform, which significantly reduces the parallelizability of the GPAW code. As a result, it is not computationally feasible to evaluate the H on graphene over Ir using the nearly physical case of 10x10 graphene units over a 9x9 slab of Ir. For this work, an 8x8 graphene lattice over a three-layer 7x7 Ir slab is used instead. This is in contrast to other reported studies that use a vdw-df functional, where a much smaller unit cell was employed. 12, 13 The optb88-vdw calculated lattice constant of graphene, a graphene-optb88-vdw = Å, defines the dimensions of the cell. The Ir slab was adapted in order to conform to the graphene lattice constant resulting in an expansion of 1.6% relative to the calculated optb88-vdw Ir lattice constant of Å. The larger lattice mismatch inherent to the slightly smaller cell size still allows the

3 graphene to easily buckle down to the Ir surface when adsorbates, such as hydrogen, interact with it. The moiré pattern with its HCP, FCC, and ATOP regions is also well reproduced. In many of the works that report DFT results using a 10x10 graphene over 9x9 Ir cell, the relaxation is performed using the LDA functional, 14, 15 a GGA functional with a semi-empirical vdw correction 16 or M06-L. 17 This work instead presents results from an approach that seamlessly integrates both the short and longrange correlation effects directly in the ab initio calculation on a nearly physically sized cell. The relaxation parameters for the presented results are as follows: cells were periodic in the two dimensions parallel to the graphene and Ir surfaces. In the perpendicular direction at least 7.5 Å separated the slab from the cell boundary. The grid spacing employed was Å. A 2x2 K-point mesh was sampled as the adsorption energy of a hydrogen cluster adsorbed onto the graphene over Ir converged there. Forces were relaxed until they were below 0.02 ev/å. In all cases, the bottom layer of Ir was kept fixed. The distribution of H atoms forming the variously sized adsorbed clusters was manually sampled assuming that the clusters tend to form symmetrically at the 17, 18 center of either FCC or HCP regions. The band structures of the optimized models were obtained by performing singlepoint calculations with the VASP code, 19, 20 using the same optb88-vdw exchangecorrelation functional and PAW method. A 4x4x1 K-point mesh was used for converging the charge density, which was kept fixed for the subsequent calculations of the eigenvalues at K-points along the Γ-K direction.

4 S2: Clean graphene on Ir(111) Figure S1: STM image showing graphene grown on Ir(111). A continuous, single crystal graphene layer is observed, U = 458 mv, I = 2.0 na, 3000Å x 3000Å. Inset: Atomically resolved STM image of graphene on Ir(111) showing the high structural quality of the graphene down to the atomic scale. The moiré unit cell is highlighted by the black box. High symmetry sites ATOP, HCP and FCC are marked by a star, square and circle, recpectively. U = -449 mv, I = 1.0 na, 132Å x 132Å. S3: Structures used for band dispersion calculation A) 3H HCP B) 6H HCP C) 3H HCP + 3H FCC Figure S2: Three systems were considered for calculating the band dispersions for hydrogenated graphene on Ir(111). A) Three H atoms on the HCP site, B) six atoms on the HCP site and B) three atoms on each of the FCC and HCP sites giving a total coverage of six atoms. For the calculation of hydrogenated freestanding graphene, the three Ir layers were removed. The hydrogen and corrugation (as can be seen in the side view) was, however, maintained. References 1. Mortensen, J. J.; Hansen, L. B.; Jacobsen, K. W. Real-Space Grid Implementation of the Projector Augmented Wave Method. Phys. Rev. B 2005, 71, Enkovaara, J.; Rostgaard, C.; Mortensen, J. J.; Chen, J.; Dulak, M.; Ferrighi, L.; Gavnholt, J.; Glinsvad, C.; Haikola, V.; Hansen, H. A.; Kristoffersen, H. H.;

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