Cross-polarized excitons in carbon nanotubes

Svetlana Kilina, Sergei Tretiak, Stephen K. Doorn, Zhengtang Luo, Fotios Papadimitrakopoulos, Andrei Piryatinski, Avadh Saxena, Alan R. Bishop

Research output: Contribution to journalArticlepeer-review

48 Citations (Scopus)


Polarization of low-lying excitonic bands in finite-size semiconducting single-walled carbon nanotubes (SWNTs) is studied by using quantum-chemical methodologies. Our calculations elucidate properties of cross-polarized excitons, which lead to the transverse optical absorption of nanotubes and presumably couple to intermediate-frequency modes recently observed in resonance Raman excitation spectroscopy. We identify up to 12 distinct excitonic transitions below the second fundamental band associated with the E22 van Hove singularity. Calculations for several chiral SWNTs distinguish the optically active "bright" excitonic band polarized parallel to the tube axis and several optically "weak" cross-polarized excitons. The rest are optically (near) forbidden "dark" transitions. An analysis of the transition density matrices related to excitonic bands provides detailed information about delocalization of excitonic wavefunction along the tube. Utilization of the natural helical coordinate system accounting for the tube chirality allows one to disentangle longitudinal and circumferential components. The distribution of the transition density matrix along a tube axis is similar for all excitons. However, four parallel-polarized excitons associated with the E11 transition are more localized along the circumference of a tube, compared with others related to the E12 and E21 cross-polarized transitions. Calculated splitting between optically active parallel- and cross-polarized transitions increases with tube diameter, which compares well with experimental spectroscopic data.

Original languageEnglish
Pages (from-to)6797-6802
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number19
Publication statusPublished - 13 May 2008
Externally publishedYes


  • Collective electronic oscillator method
  • Exciton localization
  • Helical nanotube coordinates
  • Transverse absorption


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