Energy Gaps in Graphene Nanoribbons

Details Energy Gaps in Graphene Nanoribbons Energy Gaps in Graphene Nanoribbons

2006-11-23

arxiv.org/abs/cond-mat/0611602v1

Phys. Rev. Lett. 97, 216803 (2006)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

10.1103/PhysRevLett.97.216803

Based on a first-principles approach, we present scaling rules for the band gaps of graphene nanoribbons (GNRs) as a function of their widths. The GNRs considered have either armchair or zigzag shaped edges on both sides with hydrogen passivation. Both varieties of ribbons are shown to have band gaps. This differs from the results of simple tight-binding calculations or solutions of the Dirac's equation based on them. Our {\it ab initio} calculations show that the origin of energy gaps for GNRs with armchair shaped edges arises from both quantum confinement and the crucial effect of the edges. For GNRs with zigzag shaped edges, gaps appear because of a staggered sublattice potential on the hexagonal lattice due to edge magnetization. The rich gap structure for ribbons with armchair shaped edges is further obtained analytically including edge effects. These results reproduce our {\it ab initio} calculation results very well.

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