期刊
SCIENCE AND TECHNOLOGY OF ADVANCED MATERIALS
卷 11, 期 5, 页码 -出版社
TAYLOR & FRANCIS LTD
DOI: 10.1088/1468-6996/11/5/054504
关键词
graphene; graphene nanoribbon; tight-binding model; edge orientation; edge state; analytical solution; chirality; wave mechanics
资金
- Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan [20001006]
Graphene is a one-atom-thick layer of graphite, where low-energy electronic states are described by the massless Dirac fermion. The orientation of the graphene edge determines the energy spectrum of pi-electrons. For example, zigzag edges possess localized edge states with energies close to the Fermi level. In this review, we investigate nanoscale effects on the physical properties of graphene nanoribbons and clarify the role of edge boundaries. We also provide analytical solutions for electronic dispersion and the corresponding wavefunction in graphene nanoribbons with their detailed derivation using wave mechanics based on the tight-binding model. The energy band structures of armchair nanoribbons can be obtained by making the transverse wavenumber discrete, in accordance with the edge boundary condition, as in the case of carbon nanotubes. However, zigzag nanoribbons are not analogous to carbon nanotubes, because in zigzag nanoribbons the transverse wavenumber depends not only on the ribbon width but also on the longitudinal wavenumber. The quantization rule of electronic conductance as well as the magnetic instability of edge states due to the electron-electron interaction are briefly discussed.
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