Cross-polarized excitons in carbon nanotubes

• Published in: Proceedings of the National Academy of Sciences - PNAS Vol. 105; no. 19; pp. 6797 - 6802
• Main Authors: Kilina, Svetlana, Tretiak, Sergei, Doorn, Stephen K, Luo, Zhengtang, Papadimitrakopoulos, Fotios, Piryatinski, Andrei, Saxena, Avadh, Bishop, Alan R
• Format: Journal Article
• Language: English
• Published: United States National Academy of Sciences 13.05.2008; National Acad Sciences
• Subjects: Atoms; Carbon; Carbon nanotubes; Chemistry; Chirality; Circumferences; Coordinate systems; Electrocatalysis; Electrons; Excitons; Nanotubes; Optical transition; Oscillator strengths; Physical Sciences; Spectrum analysis; Studies
• ISSN: 0027-8424; 1091-6490
• DOI: 10.1073/pnas.0711646105

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.