Edge state in graphene ribbons: Nanometer size effect and edge shape dependence

Phys. Rev. B 54, 17954 – Published 15 December 1996
Kyoko Nakada, Mitsutaka Fujita, Gene Dresselhaus, and Mildred S. Dresselhaus


Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale.

DOI: http://dx.doi.org/10.1103/PhysRevB.54.17954

  • Received 26 June 1996
  • Published in the issue dated 15 December 1996

© 1996 The American Physical Society

Authors & Affiliations

Kyoko Nakada and Mitsutaka Fujita

  • Institute of Materials Science, University of Tsukuba, Tsukuba 305, Japan

Gene Dresselhaus and Mildred S. Dresselhaus

  • Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307

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