The concept of cutting lines in carbon nanotube science

Ge G. Samsonidze, R. Saito, A. Jorio, M. A. Pimenta, A. G. Souza Filho, A. Grüneis, G. Dresselhaus, M. S. Dresselhaus

Research output: Contribution to journalReview articlepeer-review

110 Citations (Scopus)


A review is presented of one-dimensional cutting lines that are utilized to obtain the physical properties of carbon nanotubes from the corresponding properties of graphite by the zone-folding scheme. Quantization effects in general low-dimensional systems are briefly discussed, followed by a more detailed consideration of one-dimensional single-wall carbon nanotubes. The geometrical structure of the nanotube is described, from which quantum confined states are constructed. These allowed states in the momentum space of graphite are known as cutting lines. Different representations of the cutting lines in momentum space are introduced. Electronic and phonon dispersion relations for nanotubes are derived by using cutting lines and the zone-folding scheme. The relation between cutting lines and singularities in the electronic density of states is considered. The selection rules for carbon nanotubes are shown to be directly connected with the cutting lines. Different experimental techniques are considered that confirm the validity of cutting lines and the zone-folding approach.

Original languageEnglish
Pages (from-to)431-458
Number of pages28
JournalJournal of Nanoscience and Nanotechnology
Issue number6
Publication statusPublished - 2003 Dec


  • Carbon Nanotubes
  • Cutting Lines
  • Raman Scattering
  • Selection Rules
  • Zone-Folding

ASJC Scopus subject areas

  • Bioengineering
  • Chemistry(all)
  • Biomedical Engineering
  • Materials Science(all)
  • Condensed Matter Physics


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