Size and mobility of excitons in (6, 5) carbon nanotubes


Knowledge of excited-state dynamics in carbon nanotubes is determinant for their prospective use in optoelectronic applications. It is known that primary photoexcitations are quasi-one-dimensional excitons, the electron–hole correlation length (‘exciton size’) of which corresponds to a finite volume in the phase space. This volume can be directly measured by nonlinear spectroscopy provided the time resolution is short enough for probing before population relaxation. Here, we report on the experimental determination of exciton size and mobility in (6, 5) carbon nanotubes. The samples are sodium cholate suspensions of nanotubes (produced by the CoMoCat method) obtained by density-gradient ultracentrifugation. By using sub-15 fs near-infrared pulses to measure the nascent bleach of the lowest exciton resonance, we estimate the exciton size to be 2.0±0.7 nm. Exciton–exciton annihilation in our samples is found to be rather inefficient so that many excitons can coexist on a single nanotube.

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Figure 1: Two-dimensional pump–probe spectroscopy.
Figure 2: Pump intensity dependence of pump–probe kinetics.
Figure 3: Extraction of exciton size from the intensity-dependent bleach.


  1. 1

    Wang, F., Dukovic, G., Brus, L. E. & Heinz, T. F. The optical resonances in carbon nanotubes arise from excitons. Science 308, 838–841 (2005).

    ADS  Article  Google Scholar 

  2. 2

    Ando, T. Excitons in carbon nanotubes. J. Phys. Soc. Jpn 66, 1066–1073 (1997).

    ADS  Article  Google Scholar 

  3. 3

    Perebeinos, V., Tersoff, J. & Avouris, P. Scaling of excitons in carbon nanotubes. Phys. Rev. Lett. 92, 257402 (2004).

    ADS  Article  Google Scholar 

  4. 4

    Tretiak, S. et al. Excitons and Peierls distortion in conjugated carbon nanotubes. Nano Lett. 7, 86–92 (2007).

    ADS  Article  Google Scholar 

  5. 5

    Chang, E., Bussi, G., Ruini, A. & Molinari, E. Excitons in carbon nanotubes: An ab initio symmetry-based approach. Phys. Rev. Lett. 92, 196401 (2004).

    ADS  Article  Google Scholar 

  6. 6

    Korovyanko, O. J., Sheng, C.-X., Vardeny, Z.V., Dalton, A. B. & Baughman, R. H. Ultrafast spectroscopy of excitons in single-walled carbon nanotubes. Phys. Rev. Lett. 92, 017403 (2004).

    ADS  Article  Google Scholar 

  7. 7

    Cognet, L. et al. Stepwise quenching of exciton fluorescence in carbon nanotubes by single-molecule reactions. Science 316, 1465–1468 (2007).

    ADS  Article  Google Scholar 

  8. 8

    Wang, F., Dukovic, G., Knoesel, E., Brus, L. E. & Heinz, T. F. Observation of rapid Auger recombination in optically excited semiconducting carbon nanotubes. Phys. Rev. B 70, 241403(R) (2004).

    ADS  Article  Google Scholar 

  9. 9

    Ma, Y.-Z., Valkunas, 1 L., Dexheimer, S. L., Bachilo, S. M. & Fleming, G. R. Femtosecond spectroscopy of optical excitations in single-walled carbon nanotubes: Evidence for exciton–exciton annihilation. Phys. Rev. Lett. 94, 157402 (2005).

    ADS  Article  Google Scholar 

  10. 10

    Goesele, U. M. Reaction kinetics and diffusion in condensed matter. Prog. React. Kinetics 13, 63–161 (1984).

    Google Scholar 

  11. 11

    Greene, B. I., Orenstein, J. & Schmitt-Rink, S. All-optical nonlinearities in organics. Science 247, 679–687 (1990).

    ADS  Article  Google Scholar 

  12. 12

    Zhu, Z. et al. Pump-probe spectroscopy of exciton dynamics in (6, 5) carbon nanotubes. J. Phys. Chem. C 111, 3831–2825 (2007).

    Article  Google Scholar 

  13. 13

    Schmitt-Rink, S., Chemla, D. S. & Miller, D. A. B. Theory of transient excitonic optical nonlinearities in semiconductor quantum-well structures. Phys. Rev. B 32, 6601–6609 (1985).

    ADS  Article  Google Scholar 

  14. 14

    Capaz, R. B., Spataru, C. D., Beigi, S. I. & Louie, S. G. Diameter and chirality dependence of exciton properties in carbon nanotubes. Phys. Rev. B 74, 121401, R (2006).

    ADS  Article  Google Scholar 

  15. 15

    Zheng, M. & Diner, A. Solution redox chemistry of carbon nanotubes. J. Am. Chem. Soc. 126, 15490–15494 (2004).

    Article  Google Scholar 

  16. 16

    Manzoni, C. et al. Intersubband exciton relaxation dynamics in single-walled carbon nanotubes. Phys. Rev. Lett. 94, 207401 (2005).

    ADS  Article  Google Scholar 

  17. 17

    Hagen, A. et al. Phys. Rev. Lett. 95, 197401 (2005).

    ADS  Article  Google Scholar 

  18. 18

    Crochet, J., Clemens, M. & Hertel, T. Quantum yield heterogeneities of aqueous single-wall carbon nanotube suspensions. J. Am. Chem. Soc. 129, 8058–8059 (2007).

    Article  Google Scholar 

  19. 19

    Manzoni, C., Polli, D. & Cerullo, G. Two-color pump-probe system broadly tunable over the visible and the near infrared with sub-30 fs temporal resolution. Rev. Sci. Instrum. 77, 023103 (2006).

    ADS  Article  Google Scholar 

  20. 20

    Polli, D., Lüer, L. & Cerullo, G. High-time-resolution pump-probe system with broadband detection for the study of time-domain vibrational dynamics. Rev. Sci. Instrum. 78, 103108 (2007).

    ADS  Article  Google Scholar 

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This work was financially supported by the European Commission through the Human Potential Programme (Marie-Curie RTN BIMORE, Grant No. MRTN-CT-2006-035859) and by the National Science Foundation (NSF DMR-0606505). We acknowledge the financial support of the project FIRB SYNERGY.

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All authors contributed significantly to this work. In detail, project planning by G.L. and T.H., sample preparation and characterization by J.C. and T.H., measurement set-up and automation by D.P. and L.L., experiments by L.L. and S.H., data evaluation by L.L., G.L. and S.H., manuscript writing by L.L., G.L., T.H. and D.P.

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Correspondence to Larry Lüer.

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Lüer, L., Hoseinkhani, S., Polli, D. et al. Size and mobility of excitons in (6, 5) carbon nanotubes. Nature Phys 5, 54–58 (2009).

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