The finite size effects on the electronic structure of graphene ribbons are studied using first principles density functional techniques. The energy gap [difference between highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO)] dependence for finite width and length is computed for both armchair and zigzag ribbons and compared to their one-dimensional (infinite length) cases. The results suggest, in addition to quantum confinement along the width of the ribbon, an additional finite size effect emerges along the length of ribbons only for metallic armchair ribbons. The origin of additional quantum confinement in these structures is analyzed based on the energy states near the Fermi energy: both HOMO and LUMO energy levels for metallic armchair ribbons are delocalized entirely on the ribbons while for nonmetallic ribbons, these states are localized at the edges only. The results are discussed in light of effect of passivation on the electronic properties of graphenes and their impact on nanoelectronic devices based on graphenes.

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We analyze spin-dependent energetics and conductance for one dimensional (1D) atomic carbon wires consisting of terminal magnetic (Co) and interior nonmagnetic (C) atoms sandwiched between gold electrodes, obtained employing first-principles gradient corrected density functional theory and Landauer's formalism for conductance. Wires containing an even number of interior carbon atoms are found to be acetylenic with σ − π bonding patterns, while cumulene structures are seen in wires containing odd number of interior carbon atoms, as a result of strong π-conjugation. Ground states of carbon wires containing up to 13 C atoms are found to have anti-parallel spin configurations of the two terminal Co atoms, while the 14 C wire has a parallel Co spin configuration in the ground state. The stability of the anti-ferromagnetic state in the wires is ascribed to a super-exchange effect. For the cumulenic wires this effect is constant for all wire lengths. For the acetylenic wires, the superexchange effect diminishes as the wire length increases, going to zero for the atomic wire containing 14 carbon atoms. Conductance calculations at the zero bias limit show spin-valve behavior, with the parallel Co spin configuration state giving higher conductance than the corresponding anti-parallel state, and a non-monotonic variation of conductance with the length of the wires for both spin configurations.