Energy gaps in zero-dimensional graphene nanoribbons

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Abstract
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.