2006/11/23 by Young-Woo Son, Marvin L. Cohen, Steven G. Louie · 2 citations
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.mtrl-sci
paper · pdf · doi:10.1103/physrevlett.97.216803
published as Phys. Rev. Lett. 97, 216803 (2006)
arxiv created 2006/11/23 · arxiv updated 2009/12/01
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.