We present a tight-binding theory of the Dirac point resonances due to adsorbed atoms and molecules on an infinite two-dimensional graphene sheet based on the standard tight-binding model of the graphene $\pi$-band electronic structure and the extended Hückel model of the adsorbate and nearby graphene carbon atoms. The relaxed atomic geometries of the adsorbates and graphene are calculated using density functional theory. Our model includes the effects of local rehybridization of the graphene from the ${\mathit{sp}}^2$ to ${\mathit{sp}}^3$ electronic structures that occurs when adsorbed atoms or molecules bond covalently to the graphene. Unlike in previous tight-binding models of Dirac point resonances, adsorbed species with multiple extended molecular orbitals and bonding to more than one graphene carbon atom are treated. More accurate and more general analytic expressions for the Green’s function matrix elements that enter the $T$-matrix theory of Dirac point resonances than have been available previously are obtained. We study H, F, OH, and O adsorbates on graphene and for each we find a strong scattering resonance (two resonances for O) near the Dirac point of graphene, by far the strongest and closest to the Dirac point being the resonance for H. We extract a minimal set of tight-binding parameters that can be used to model resonant electron scattering and electron transport in graphene and graphene nanostructures with adsorbed H, F, OH, and O accurately and efficiently. We also compare our results for the properties of Dirac point resonances due to adsorbates on graphene with those obtained by others using density-functional-theory-based electronic structure calculations and discuss their relative merits. We then present calculations of electronic quantum transport in graphene nanoribbons with these adsorbed species. Our transport calculations capture the physics of the scattering resonances that are induced in the graphene ribbons near the Dirac point by the presence of the adsorbates. We find that the Dirac point resonances play a dominant role in quantum transport in ribbons with adsorbates: Even at low adsorbate concentrations the conductance of the ribbon is strongly suppressed and a transport gap develops for electron Fermi energies near the resonance. The transport gap is centered very near the Dirac point energy for H, below it for F and OH, and above it for O. We find conduction in ribbons with adsorbed H atoms to be very similar to that in ribbons with equal concentrations of carbon atom vacancies. We predict ribbons with adsorbed H, F, OH, and O, under appropriate conditions, to exhibit quantized conductance steps of equal height, similar to those that have been observed by Lin et al. [Phys. Rev. B 78, 161409(R) (2008)] at moderately low temperatures, even for ribbons with conductances a few orders of magnitude smaller than $2e^2/h$.

• Received 21 August 2010

DOI:https://doi.org/10.1103/PhysRevB.83.245442