Characterization of a Single Metal Impurity in Graphene

1. Characterization of a Single Metal Impurity in Graphene Eric Cockayne Ceramics Division, NIST, Gaithersburg Gregory M. Rutter Joseph A. Stroscio Center Nanoscale Science & Technology, NIST

2. Castro-Neto, Nature Mater. 6, 176 (2007). Castro-Neto et al., Physics World (2006) Graphene: Unusual electronic structure makes it a promising candidate For applications Microelectronics: high carrier mobility → high speed devices Resistance standard → unusual quantum Hall effect

3. Growth of graphene from by thermal desorption of Si from SiC leads to large area of graphene, but defects frequently observed Goal of this talk: elucidate nature of defects with the ultimate aim of reducing or eliminating the defects In particular, will focus in pseudo-six fold defect very commonly observed Properties of defect found in STM images: Near sixfold symmetry; actually threefold Sqrt(3) modulation of graphene lattice Center of defect is dark Dark spokes observed. Depending on imaging conditions, diameter around 20-30 Ang.

4. dI/dV plot ~ local density of states sharply peaked in energy, about 0.5 eV above the Dirac point

5. Methods: ab initio & tight binding Ab initio electronic structure VASP used DFT, ultrasoft pseudopotentials 212 eV plane wave cutoff; 324 and 432 supercells for bilayer 8748 k points per BZ of primitive cell STM topographs simulations Tersoff approximation: fixed V current proportional to local density of states between Fermi level and bias V Tight binding electronic structure Mo d levels and C 2p z levels put into model Tight binding parameters determined via least squares Fitting to ab initio data Up to 3888 atoms for bilayer supercell ~175000 k points in primitive BZ cell

6. Based on pseudosixfold nature of defect and fact that it is only observed in graphene bilayers/multilayers, hypothesize that defect is on axis of the center of a hexagon in the topmost layer of Bernal stacked graphene Intercalation Adatom Substitution Defect atom can be anything: focus on Mo and Si

7. Graphene layers remain nearly flat (Dh < 0.25 Ang) for intercalated Mo Magnetism? Mo position Magnetic moment isolated atom 6.0 adatom 0.0 intercalated 0.0 substitution 2.0

11. Bilayer Trilayer

12. Tight binding model Include only C 2pz & Mo 4d orbitals Intralayer C-C coupling to 2 neighbor; interlayer coupling for A sublattice Mo-C coupling terms to 10 neighbors shown Parameters found by least square fitting to ab initio data Variance of C-C interations essential: For these terms: model A = Aideal + B(d – dideal); where A, B fit to each C-C interaction parameter; guarantees correct results reproduced for ideal graphene For larger supercells, graphene distorted around Mo as in ab initio results; rest of structure “padded” with ideal graphene.

16. Conclusions • Single intercalated metal impurity explains most of features of experimental pseudo-six-fold defect • Coupling of Mo d states with graphene 2pz states responsible • Localization plots created • Tight binding model created; surprisingly large supercells necessary for convergence