Hidden Kekulé ordering of adatoms on graphene

Abstract

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.

Heavy going

“…Cheianov et al proposed the following microscopic mechanism to open a Kekulé gap in graphene 5,6 . The enlarged unit cell of graphene with the Kekulé pattern can be pictured by tiling the honeycomb lattice with a three-colour code; say red, blue and green.…”

“…The enlarged unit cell of graphene with the Kekulé pattern can be pictured by tiling the honeycomb lattice with a three-colour code; say red, blue and green. If a dilute density of adatoms is then randomly placed on the graphene at high temperature, the system would minimize its free energy by optimizing two free-energy gains against one free-energy loss below some ordering temperature 5,6 . An electronic energy is gained by opening a Kekulé bandgap at the two inequivalent Dirac points of graphene.…”

“…Using scanning tunnelling microscopy (STM)-based techniques, Gutiŕrez et al show that the microscopic mechanism previously proposed 5,6 to open a Kekulé gap can work at temperatures extending up to 300 K (see Ref. 1).…”

Patterns of Organics on Substrates with Metallic Surface States: Why?, So??

“…Instead, q F is replaced by an ultraviolet momentum cutoff for single-layer graphene q c which is taken as the inverse lattice constant, so 4.07 nm −1 [16]. In another study, ordered arrangements of widely separated adatoms can be predicted [17]. If atoms couple to atop sites, then the exchange coupling between them decays like d −3 [17][18][19] but with a different oscillatory factor and a prefactor that is +1 (−1) if the atoms are on the same (different) Bravais sublattices [10].…”

“…In another study, ordered arrangements of widely separated adatoms can be predicted [17]. If atoms couple to atop sites, then the exchange coupling between them decays like d −3 [17][18][19] but with a different oscillatory factor and a prefactor that is +1 (−1) if the atoms are on the same (different) Bravais sublattices [10]. For undoped and doped graphene, a rich variety of analytic behaviors have been tabulated [20].…”