Trigonal anisotropy in graphite and carbon nanotubes

R. Saito, J. Jiang, A. Gruneis, K. Sato, Y. Oyama, Ge G. Samsonidze, S. G. Chou, G. Dresselhaus, M. S. Dresselhaus, L. G. Cancado, C. Fantini, A. Jorio, M. A. Pimenta

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We discuss here how the trigonal warping effect of the electronic structure is relevant to optical processes in graphite and carbon nanotubes. The electron-photon, electron-phonon, and elastic scattering matrix elements have a common factor of the coefficients of Bloch wave funtions of the A and B atoms in the graphite unit cell. Because of the three fold symmetry around the Fermi energy point (the K or K′ point), the matrix elements show a trigonal anisotropy which can be observed in both resonance Raman and photoluminescence spectroscopy. This anisotropy is essential for understanding the chirality dependence of the Raman intensity and the optical response of single wall carbon nanotubes.

Original languageEnglish
Pages (from-to)287-294
Number of pages8
JournalMolecular crystals and liquid crystals
Issue number1
Publication statusPublished - 2006 Oct 1


  • Carbon nanotubes
  • Electron-phonon interaction
  • Electron-photon interaction
  • Graphite
  • Optical response
  • Resonance Raman spectroscopy
  • Trigonal warping

ASJC Scopus subject areas

  • Chemistry(all)
  • Materials Science(all)
  • Condensed Matter Physics


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