Skip to main content

Percolation and tunneling in the quantum hall effect

  • Conference paper
  • First Online:
Non-Linearity and Breakdown in Soft Condensed Matter

Part of the book series: Lecture Notes in Physics ((LNP,volume 437))

Abstract

The question of localization in the quantum Hall system is very close to a classical percolation problem. The dominating quantum correction to this picture is tunneling. We show how this effect changes the universality class of the localization problem from that of percolation to a different one. Our result is in agreement with both experimental and numerical results.

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.

References

  1. K. v. Klitzing, G. Dorda and M. Pepper, Phys. Rev. Lett. 45, 494 (1980).

    Article  Google Scholar 

  2. R. E. Prange and S. M. Girvin, editors, The Quantum Hall Effect (Springer Verlag, Berlin, 1987).

    Google Scholar 

  3. D. C. Tsui, H. L. Störmer and S. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982).

    Article  Google Scholar 

  4. S. Koch, R. J. Haug, K. v. Klitzing, and K. Ploog, Phys. Rev. Lett. 67, 883 (1991).

    Article  PubMed  Google Scholar 

  5. H. P. Wei, D. C. Tsui, and A. M. M. Pruisken, Phys. Rev. B 33,1488 (1985); H. P. Wei, D. C. Tsui, M. A. Paalanen, and A. M. M. Pruisken, Phys. Rev. Lett. 61, 1294 (1988); L. Engel, H. P. Wei, D. C. Tsui, and M. Shayegan, Surf. Sci. 229, 13 (1990); S. Koch, R. J. Haug, K. v. Klitzing, and K. Ploog, Phys. Rev. Lett. 67, 883 (1991).

    Article  Google Scholar 

  6. J. T. Chalker and P. D. Coddington, J. Phys. C 21, 2665 (1988); B. Huckestein and B. Kramer, Phys. Rev. Lett. 64,1437 (1990); D. K. K. Lee and J. T. Chalker, Phys. Rev. Lett. 72, 1510 (1994).

    Google Scholar 

  7. B. Huckestein and B. Kramer, Phys. Rev. Lett. 64, 1437 (1990).

    Article  PubMed  Google Scholar 

  8. G. V. Mil'nikov and I. M. Sokolov, JETP Letters 48, 536 (1988).

    Google Scholar 

  9. A. Hansen and C. A. Lötken, preprint, 1993.

    Google Scholar 

  10. D. Stauffer and A. Aharony, Introduction to Percolation Theory 2. ed. (Taylor and Francis, London, 1992).

    Google Scholar 

  11. R. F. Kazarinov and S. Luryi, Phys. Rev. B 25, 7626 (1982).

    Article  Google Scholar 

  12. S. A. Trugman, Phys. Rev. B 27, 7539 (1983).

    Article  Google Scholar 

  13. E. Abrahams, P. W. Anderson, D. C. Licciardello and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).

    Article  Google Scholar 

  14. M. P. M. den Nijs, J. Phys. A: Math. Gen. 12, 1857 (1979); J. L. Black and V. J. Emery, Phys. Rev. B 23, 429 (1981).

    Article  Google Scholar 

  15. M. Tsukada, J. Phys. Soc. Japan, 41, 1466 (1976).

    Article  Google Scholar 

  16. B. I. Halperin, Phys. Rev. B 25, 2185 (1982).

    Article  Google Scholar 

  17. M. Büttiker, Phys. Rev. B 38, 9375 (1988).

    Article  Google Scholar 

  18. F. Maaø, A. Bobylev, A. Hansen and E. H. Hauge, preprint, 1994.

    Google Scholar 

  19. D. ter Haar, Selected Problems in Quantum Mechanics (Infosearch, London, 1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Kamal K. Bardhan Bikas K. Chakrabarti Alex Hansen

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag

About this paper

Cite this paper

Hansen, A. (1994). Percolation and tunneling in the quantum hall effect. In: Bardhan, K.K., Chakrabarti, B.K., Hansen, A. (eds) Non-Linearity and Breakdown in Soft Condensed Matter. Lecture Notes in Physics, vol 437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58652-0_46

Download citation

  • DOI: https://doi.org/10.1007/3-540-58652-0_46

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58652-4

  • Online ISBN: 978-3-540-49037-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics