Energy Gaps in Graphene Nanoribbons

Young-Woo Son, Marvin L. Cohen, and Steven G. Louie
Phys. Rev. Lett. 97, 216803 – Published 22 November 2006; Erratum Phys. Rev. Lett. 98, 089901 (2007)

Abstract

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 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 ab initio calculation results very well.

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  • Received 29 June 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.216803

©2006 American Physical Society

Erratum

Erratum: Energy Gaps in Graphene Nanoribbons [Phys. Rev. Lett. 97, 216803 (2006)]

Young-Woo Son, Marvin L. Cohen, and Steven G. Louie
Phys. Rev. Lett. 98, 089901 (2007)

Authors & Affiliations

Young-Woo Son, Marvin L. Cohen, and Steven G. Louie*

  • Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
  • Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

  • *Electronic address: sglouie@berkeley.edu

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Issue

Vol. 97, Iss. 21 — 24 November 2006

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