Partial Kekule Ordering of Adatoms on Graphene

Electronic and transport properties of Graphene, a one-atom thick crystalline material, are sensitive to the presence of atoms adsorbed on its surface. An ensemble of randomly positioned adatoms, each serving as a scattering center, leads to the Bolzmann-Drude diffusion of charge determining the resistivity of the material. An important question, however, is whether the distribution of adatoms is always genuinely random. In this Article we demonstrate that a dilute adatoms on graphene may have a tendency towards a spatially correlated state with a hidden Kekulé mosaic order. This effect emerges from the interaction between the adatoms mediated by the Friedel oscillations of the electron density in graphene. The onset of the ordered state, as the system is cooled below the critical temperature, is accompanied by the opening of a gap in the electronic spectrum of the material, dramatically changing its transport properties. Physics Department, Lancaster University, Lancaster LA1 4YB, UK Department of Physics, University of Oslo, PO Box 1048 Blindern, N-0316 Oslo, Norway Physics Department, Columbia University, 538 West 120th Street, New York, NY 10027, USA 1 When can an apparently random system be considered ordered? Or can an apparently random ensemble of impurities in a system be correlated enough to force the reconstruction of the electronic band structure in a material? In this Article we predict that a dilute ensemble of adatoms sprinkled randomly over a graphene monolayer [1, 2] can establish long-range correlations between their positions, despite the fact that they may be many graphene unit-cell lengths apart. This correlation is strong enough that at a transition temperature it will induce an energy gap in the electronic spectrum despite the fact that, in the “ordered” state, the distribution of adatoms does not show any crystalline structure. It rather resembles the ferromagnetically ordered state of spins of magnetic ions in dilute magnetic semiconductors [3]. The physical mechanism behind this phenomenon is the electron-mediated interaction between the adsorbents, which prompts their partial ordering into a configurations associated with a hexagonal superlattice with a unit cell three times bigger than that of graphene. Since the density, ρ of adsorbents is low, they occupy a small randomly chosen fraction of the equivalent positions on the superlattice. This ordering folds the Brillouin zone and thus opens a spectral gap for low-energy electrons. This phenomenon suggests a novel route towards engineering the band structure and controlling transport in graphene-based devices. Graphene [4, 2] is a two dimensional crystal of carbon atoms, which form a honeycomb lattice with two distinct sublattices (A and B). The first Brillouin zone (BZ) has a hexagonal form (the blue area in Fig. 1A), and the conduction band touches the valence band in six BZ corners [4] which form two non-equivalent triads of BZ corners, K and K connected by the reciprocal lattice vectors, G and G. Low-energy elec-