Skip to main content

Luttinger liquid behavior in carbon nanotubes

  • Carbon Nanotubes
  • Conference paper
  • First Online:
Advances in Solid State Physics 40

Part of the book series: Advances in Solid State Physics ((ASSP,volume 40))

Abstract

The low-energy theory of metallic carbon nanotubes is derived by bosonization methods. For single-wall nanotubes, the electron-electron interaction destroys the Fermi liquid state and leads to Luttinger liquid behavior. For individual multi-wall nanotubes or a rope of single-wall nanotubes, correlations are also important and can imply Luttinger liquid behavior again. Characteristic Luttinger liquid power laws are found for the tunneling density of states and the linear conductance in the presence of a backscatterer, with exponents approaching their Fermi liquid value only very slowly as the number of conducting shells or tubes increases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. S. Iijima, Nature 354, 56 (1991).

    Article  ADS  Google Scholar 

  2. N. Hamada, S. Sawada, and A. Oshiyama, Phys. Rev. Lett. 68, 1579 (1992).

    Article  ADS  Google Scholar 

  3. J.W.G. Wildöer, L.C. Venema, A.G. Rinzler, R.G. Smalley, and C. Dekker, Nature 391, 59 (1998); T.W. Odom, J. Huang, P. Kim, and C.M. Lieber, ibid Nature 391, 62, (1998).

    Article  ADS  Google Scholar 

  4. S.J. Tans, M.H. Devoret, H. Dai, A. Thess, R.E. Smalley, L.J. Geerligs, and C. Dekker, Nature 386, 474 (1997).

    Article  ADS  Google Scholar 

  5. S.J. Tans, M.H. Devoret, R.J.A. Groeneveld, and C. Dekker, Nature 394, 761 (1998).

    Article  ADS  Google Scholar 

  6. For a recent perspective, see, A.O. Gogolin, A.A. Nersesyan, and A.M. Tsvelik, Bosonization and Strongly Correlated Systems (Cambridge University Press, 1998).

    Google Scholar 

  7. C.L. Kane and M.P.A. Fisher, Phys. Rev. B 46, 15 233 (1992).

    Google Scholar 

  8. R. Egger and A.O. Gogolin, Phys. Rev. Lett. 79, 5082 (1997); Eur. Phys. J B 3, 281 (1998).

    Article  ADS  Google Scholar 

  9. C.L. Kane, L. Balents, and M.P.A. Fisher, Phys. Rev. Lett. 79, 5086 (1997).

    Article  ADS  Google Scholar 

  10. Z. Yao, H.W.Ch. Postma, L. Balents, and C. Dekker, Nature 402, 273 (1999).

    Article  ADS  Google Scholar 

  11. A. Bachtold, C. Strunk, J.P. Salvetat, J.M. Bonard, L. Forró, T. Nussbaumer, and C. Schönenberger, Nature 397, 673 (1999); C. Schönenberger, A. Bachtold, C. Strunk, J.P. Salvetat, and L. Forró, Appl. Phys. A 69, 283 (1999).

    Article  ADS  Google Scholar 

  12. A.Yu. Kasumov, H. Bouchiat, B. Reulet, O. Stephan, I.I. Khodos, Yu.B. Gorbatov, and C. Colliex, Europhys. Lett. 43, 89 (1998).

    Article  ADS  Google Scholar 

  13. M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, and P.L. McEuen, Nature 397, 598 (1999).

    Article  ADS  Google Scholar 

  14. R. Egger, Phys. Rev. Lett. 83, 5547 (1999).

    Article  ADS  Google Scholar 

  15. S. Frank, P. Poncharal, Z.L. Wang, and W.A. de Heer, Science 280, 1744 (1998).

    Article  ADS  Google Scholar 

  16. T. Hertel, R.E. Walkup, and Ph. Avouris, Phys. Rev. B 58, 13870 (1998).

    Article  ADS  Google Scholar 

  17. C.L. Kane and E.J. Mele, Phys. Rev. Lett. 78, 1932 (1997).

    Article  ADS  Google Scholar 

  18. A.A. Maarouf, C.L. Kane, and E.J. Mele, preprint cond-mat/0001300.

    Google Scholar 

  19. K.A. Matveev and L.I. Glazman, Phys. Rev. Lett. 70, 990 (1993).

    Article  ADS  Google Scholar 

  20. P. Delaney, H.J. Choi, J. Ihm, S.G. Louie, and M.L. Cohen, Nature 391, 466 (1998).

    Article  ADS  Google Scholar 

  21. C.T. White and T.N. Todorov, Nature 393, 240 (1998).

    Article  ADS  Google Scholar 

  22. J.C. Charlier and J.P. Michenaud, Phys. Rev. Lett. 70, 1858 (1993).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bernhard Kramer

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

About this paper

Cite this paper

Egger, R. (2000). Luttinger liquid behavior in carbon nanotubes. In: Kramer, B. (eds) Advances in Solid State Physics 40. Advances in Solid State Physics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108356

Download citation

  • DOI: https://doi.org/10.1007/BFb0108356

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41576-3

  • Online ISBN: 978-3-540-44560-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics