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An atlas of carbon nanotube optical transitions

Nature Nanotechnology volume 7, pages 325–329 (2012)Cite this article

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Abstract

Electron–electron interactions are significantly enhanced in one-dimensional systems1, and single-walled carbon nanotubes provide a unique opportunity for studying such interactions and the related many-body effects in one dimension2,3,4. However, single-walled nanotubes can have a wide range of diameters and hundreds of different structures, each defined by its chiral index (n,m)5,6, where n and m are integers that can have values from zero up to 30 or more. Moreover, one-third of these structures are metals and two-thirds are semiconductors, and they display optical resonances at many different frequencies. Systematic studies of many-body effects in nanotubes would therefore benefit from the availability of a technique for identifying the chiral index of a nanotube based on a measurement of its optical resonances, and vice versa. Here, we report the establishment of a structure–property ‘atlas’ for nanotube optical transitions based on simultaneous electron diffraction measurements of the chiral index and Rayleigh scattering measurements of the optical resonances7,8 of 206 different single-walled nanotube structures. The nanotubes, which were suspended across open slit structures on silicon substrates, had diameters in the range 1.3–4.7 nm. We also use this atlas as a starting point for a systematic study of many-body effects in the excited states of single-walled nanotubes9,10,11,12,13,14,15,16. We find that electron–electron interactions shift the optical resonance energies by the same amount for both metallic and semiconducting nanotubes, and that this shift (which corresponds to an effective Fermi velocity renormalization) increases monotonically with nanotube diameter. This behaviour arises from two sources: an intriguing cancellation of long-range electron–electron interaction effects, and the dependence of short-range electron–electron interactions on diameter10,11.

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Figure 1: Electron diffraction patterns and Rayleigh spectra of three representative nanotubes.
Figure 2: Momentum-resolved transitions with nanotube optical resonances.
Figure 3: Renormalization of the effective Fermi velocity and its p-dependence.
Figure 4: Trigonal asymmetry.

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References

  1. Voit, J. One-dimensional Fermi liquids. Rep. Prog. Phys. 58, 977–1116 (1995).

    Article  CAS  Google Scholar 

  2. Bockrath, M. et al. Luttinger-liquid behaviour in carbon nanotubes. Nature 397, 598–601 (1999).

    Article  CAS  Google Scholar 

  3. Odom, T. W., Huang, J. L., Cheung, C. L. & Lieber, C. M. Magnetic clusters on single-walled carbon nanotubes: the Kondo effect in a one-dimensional host. Science 290, 1549–1552 (2000).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. Saito, R., Dresselhaus, G. & Dresselhaus, M. S. Physical Properties of Carbon Nanotubes (Imperial College Press, 1998).

  6. Reich, S., Thomsen, C. & Maultzsch, J. Carbon Nanotubes: Basic Concepts and Physical Properties (Wiley, 2004).

  7. Sfeir, M. Y. et al. Probing electronic transitions in individual carbon nanotubes by Rayleigh scattering. Science 306, 1540–1543 (2004).

    Article  CAS  Google Scholar 

  8. Sfeir, M. Y. et al. Optical spectroscopy of individual single-walled carbon nanotubes of defined chiral structure. Science 312, 554–556 (2006).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  10. Kane, C. L. & Mele, E. J. Ratio problem in single carbon nanotube fluorescence spectroscopy. Phys. Rev. Lett. 90, 207401 (2003).

    Article  CAS  Google Scholar 

  11. Kane, C. L. & Mele, E. J. Electron interactions and scaling relations for optical excitations in carbon nanotubes. Phys. Rev. Lett. 93, 197402 (2004).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  13. Spataru, C. D., Ismail-Beigi, S., Benedict, L. X. & Louie, S. G. Excitonic effects and optical spectra of single-walled carbon nanotubes. Phys. Rev. Lett. 92, 077402 (2004).

    Article  Google Scholar 

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

    Article  Google Scholar 

  15. Zhao, H. B. & Mazumdar, S. Electron–electron interaction effects on the optical excitations of semiconducting single-walled carbon nanotubes. Phys. Rev. Lett. 93, 157402 (2004).

    Article  Google Scholar 

  16. Wang, F. et al. Observation of excitons in one-dimensional metallic single-walled carbon nanotubes. Phys. Rev. Lett. 99, 227401 (2007).

    Article  Google Scholar 

  17. Bachilo, S. M. et al. Structure-assigned optical spectra of single-walled carbon nanotubes. Science 298, 2361–2366 (2002).

    Article  CAS  Google Scholar 

  18. Lefebvre, J., Fraser, J. M., Homma, Y. & Finnie, P. Photoluminescence from single-walled carbon nanotubes: a comparison between suspended and micelle-encapsulated nanotubes. Appl. Phys. A 78, 1107–1110 (2004).

    Article  CAS  Google Scholar 

  19. Fantini, C. et al. Optical transition energies for carbon nanotubes from resonant Raman spectroscopy: environment and temperature effects. Phys. Rev. Lett. 93, 147406 (2004).

    Article  CAS  Google Scholar 

  20. Telg, H. et al. Chirality distribution and transition energies of carbon nanotubes. Phys. Rev. Lett. 93, 177401 (2004).

    Article  CAS  Google Scholar 

  21. Araujo, P. T. et al. Third and fourth optical transitions in semiconducting carbon nanotubes. Phys. Rev. Lett. 98, 067401 (2007).

    Article  Google Scholar 

  22. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    Article  CAS  Google Scholar 

  23. Zhang, Y. B., Tan, Y. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005).

    Article  CAS  Google Scholar 

  24. Blase, X., Benedict, L. X., Shirley, E. L. & Louie, S. G. Hybridization effects and metallicity in small radius carbon nanotubes. Phys. Rev. Lett. 72, 1878–1881 (1994).

    Article  CAS  Google Scholar 

  25. Kane, C. L. & Mele, E. J. Size, shape, and low energy electronic structure of carbon nanotubes. Phys. Rev. Lett. 78, 1932–1935 (1997).

    Article  CAS  Google Scholar 

  26. Reich, S., Thomsen, C. & Ordejon, P. Electronic band structure of isolated and bundled carbon nanotubes. Phys. Rev. B 65, 155411 (2002).

    Article  Google Scholar 

  27. Huang, S. M., Cai, X. Y. & Liu, J. Growth of millimeter-long and horizontally aligned single-walled carbon nanotubes on flat substrates. J. Am. Chem. Soc. 125, 5636–5637 (2003).

    Article  CAS  Google Scholar 

  28. Liu, K. H. et al. Intrinsic radial breathing oscillation in suspended single-walled carbon nanotubes. Phys. Rev. B 83, 113404 (2011).

    Article  Google Scholar 

  29. Liu, Z. J. & Qin, L-C. A direct method to determine the chiral indices of carbon nanotubes. Chem. Phys. Lett. 408, 75–79 (2005).

    Article  CAS  Google Scholar 

  30. Liu, K. H. et al. Direct determination of atomic structure of large-indexed carbon nanotubes by electron diffraction: application to double-walled nanotubes. J. Phys. D 42, 125412 (2009).

    Article  Google Scholar 

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Acknowledgements

This study was supported by the US National Science Foundation (NSF, CAREER grant 0846648, DMR10-1006184 and EEC-0832819 to the NSF Center for Integrated Nanomechanical Systems), the US Department of Energy (DOE, DE-AC02-05CH11231 and DE-AC02-05CH11231 to the Molecular Foundry), the National Natural Science Foundation of China (91021007, 10874218, 10974238, 20973195 and 50725209) and the Chinese Ministry of Science and Technology (2009DFA01290). Computational resources were provided by the NSF (through TeraGrid resources at the National Institute for Computational Sciences) and the DOE (through the National Energy Research Scientific Computing Centre at the Lawrence Berkeley National Laboratory). R.B.C. acknowledges support from Brazilian funding agencies CNPq, FAPERJ and INCT – Nanomateriais de Carbono.

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Authors and Affiliations

  1. Department of Physics, University of California at Berkeley, Berkeley, 94720, California, USA

    Kaihui Liu, Jack Deslippe, Fajun Xiao, Rodrigo B. Capaz, Xiaoping Hong, Alex Zettl, Steven G. Louie & Feng Wang

  2. Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Kaihui Liu, Wenlong Wang & Xuedong Bai

  3. Materials Science Division, Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA

    Jack Deslippe, Alex Zettl, Steven G. Louie & Feng Wang

  4. School of Science, Northwestern Polytechnic University, Xi'an, 710072, China

    Fajun Xiao

  5. Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972, Brazil

    Rodrigo B. Capaz

  6. The Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, 94720, California, USA

    Shaul Aloni

  7. International Center for Quantum Materials, School of Physics, Peking University, Beijing, 100871, China

    Enge Wang

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  1. Kaihui Liu
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Contributions

F.W., E.W. and K.L. conceived the experiment. K.L., F.X., X.H. and F.W. carried out the optical measurements. K.L., S.A. and X.B. carried out structural characterization. K.L., W.W. and A.Z. contributed to growing the sample. J.D., R.B.C., S.G.L. and F.W. performed theoretical analysis. All authors discussed the results and wrote the paper.

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Correspondence to Enge Wang or Feng Wang.

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The authors declare no competing financial interests.

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Liu, K., Deslippe, J., Xiao, F. et al. An atlas of carbon nanotube optical transitions. Nature Nanotech 7, 325–329 (2012). https://doi.org/10.1038/nnano.2012.52

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