Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

The microscopic nature of localization in the quantum Hall effect

Nature volume 427, pages 328–332 (2004)Cite this article

Abstract

The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field1. The effect involves exact quantization of all the electronic transport properties owing to particle localization. In the conventional theory of the quantum Hall effect, strong-field localization is associated with a single-particle drift motion of electrons along contours of constant disorder potential2. Transport experiments that probe the extended states in the transition regions between quantum Hall phases have been used to test both the theory and its implications for quantum Hall phase transitions. Although several experiments3,4,5,6,7,8,9 on highly disordered samples have affirmed the validity of the single-particle picture, other experiments10,11,12 and some recent theories13,14,15 have found deviations from the predicted universal behaviour. Here we use a scanning single-electron transistor to probe the individual localized states, which we find to be strikingly different from the predictions of single-particle theory. The states are mainly determined by Coulomb interactions, and appear only when quantization of kinetic energy limits the screening ability of electrons. We conclude that the quantum Hall effect has a greater diversity of regimes and phase transitions than predicted by the single-particle framework. Our experiments suggest a unified picture of localization in which the single-particle model is valid only in the limit of strong disorder.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Measurements of the derivative dµ/dVBG at an arbitrary position above the 2DES as function of magnetic field (B) and density (n).
Figure 2: Theoretical models for localized states.
Figure 3: Spatial scans of localized states.
Figure 4: Localized states in the presence of strong disorder.

Similar content being viewed by others

References

  1. Prange, R. E. & Girvin, S. M. The Quantum Hall Effect (Springer, New York, 1990)

    Book  Google Scholar 

  2. Huckestein, B. Scaling theory of the integer quantum Hall-effect. Rev. Mod. Phys. 67, 357–396 (1995)

    Article  ADS  CAS  Google Scholar 

  3. Wei, H., Tsui, D., Paalanen, M. & Pruisken, A. Experiments on delocalization and universality in the integral quantum Hall effect. Phys. Rev. Lett. 61, 1294–1296 (1988)

    Article  ADS  CAS  PubMed  Google Scholar 

  4. Wei, H. P., Lin, S. Y., Tsui, D. C. & Pruisken, A. M. M. Effect of long-range potential fluctuations on scaling in the integer quantum Hall-effect. Phys. Rev. B 45, 3926–3928 (1992)

    Article  ADS  CAS  Google Scholar 

  5. Engel, L., Wei, H. P., Tsui, D. C. & Shayegan, M. Critical exponent in the fractional quantum Hall-effect. Surf. Sci. 229, 13–15 (1990)

    Article  ADS  CAS  Google Scholar 

  6. Koch, S., Haug, R., von-Klitzing, K. & Ploog, K. Size-dependent analysis of the metal-insulator transition in the integral quantum Hall effect. Phys. Rev. Lett. 67, 883–886 (1991)

    Article  ADS  CAS  PubMed  Google Scholar 

  7. Engel, L. W., Shahar, D., Kurdak, C. & Tsui, D. C. Microwave frequency-dependence of integer quantum Hall-effect—evidence for finite-frequency scaling. Phys. Rev. Lett. 71, 2638–2641 (1993)

    Article  ADS  CAS  PubMed  Google Scholar 

  8. Hohls, F., Zeitler, U. & Haug, R. Hopping conductivity in the quantum Hall effect: Revival of universal scaling. Phys. Rev. Lett. 88, 1–4 (2002)

    Article  Google Scholar 

  9. Hohls, F. et al. Dynamical scaling of the quantum Hall plateau transition. Phys. Rev. Lett. 89, 1–4 (2002)

    Article  Google Scholar 

  10. Shahar, D. et al. A new transport regime in the quantum Hall effect. Solid State Commun. 107, 19–23 (1998)

    Article  ADS  CAS  Google Scholar 

  11. Balaban, N., Meirav, U. & Bar-Joseph, I. Absence of scaling in the integer quantum Hall effect. Phys. Rev. Lett. 81, 4967–4970 (1998)

    Article  ADS  CAS  Google Scholar 

  12. Cobden, D. H., Barnes, C. H. W. & Ford, C. J. B. Fluctuations and evidence for charging in the quantum Hall effect. Phys. Rev. Lett. 82, 4695–4698 (1999)

    Article  ADS  CAS  Google Scholar 

  13. Chklovskii, D. B. & Lee, P. A. Transport properties between quantum Hall plateaus. Phys. Rev. B 48, 18060–18078 (1993)

    Article  ADS  CAS  Google Scholar 

  14. Cooper, N. R. & Chalker, J. T. Coulomb interactions and the integer quantum Hall-effect—screening and transport. Phys. Rev. B 48, 4530–4544 (1993)

    Article  ADS  CAS  Google Scholar 

  15. Ruzin, I., Cooper, N. & Halperin, B. Nonuniversal behavior of finite quantum Hall systems as a result of weak macroscopic inhomogeneities. Phys. Rev. B 53, 1558–1572 (1996)

    Article  ADS  CAS  Google Scholar 

  16. Ilani, S., Yacoby, A., Mahalu, D. & Shtrikman, H. Unexpected behavior of the local compressibility near the B = 0 metal-insulator transition. Phys. Rev. Lett. 84, 3133–3136 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  17. Yoo, M. J. et al. Scanning single-electron transistor microscopy: Imaging individual charges. Science 276, 579–582 (1997)

    Article  CAS  PubMed  Google Scholar 

  18. Yacoby, A., Hess, H. F., Fulton, T. A., Pfeiffer, L. N. & West, K. W. Electrical imaging of the quantum Hall state. Solid State Commun. 111, 1–13 (1999)

    Article  ADS  CAS  Google Scholar 

  19. Zhitenev, N. B. et al. Imaging of localized electronic states in the quantum Hall regime. Nature 404, 473–476 (2000)

    Article  ADS  CAS  PubMed  Google Scholar 

  20. Ilani, S., Yacoby, A., Mahalu, D. & Shtrikman, H. Microscopic structure of the metal-insulator transition in two dimensions. Science 292, 1354–1357 (2001)

    Article  ADS  CAS  PubMed  Google Scholar 

  21. Efros, A. L. & Ioffe, A. F. Nonlinear screening and the background density of 2DEG states in magnetic field. Solid State Commun. 67, 1019–1022 (1988)

    Article  ADS  Google Scholar 

  22. Efros, A. L., Pikus, F. G. & Burnett, V. G. Density of states of a two-dimensional electron gas in a long-range random potential. Phys. Rev. B 47, 2233–2243 (1993)

    Article  ADS  CAS  Google Scholar 

  23. Shashkin, A. et al. Percolation metal-insulator transitions in the two-dimensional electron system of AlGaAs/GaAs heterostructures. Phys. Rev. Lett. 73, 3141–3144 (1994)

    Article  ADS  CAS  PubMed  Google Scholar 

  24. Kukushkin, I., Fal'ko, V., Haug, R., von Klitzing, K. & Eberl, K. Magneto-optical evidence of the percolation nature of the metal-insulator transition in the two-dimensional electron system. Phys. Rev. B 53, R13260–R13263 (1996)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We benefited from discussions with A. M. Fink'elstein, Y. Gefen, Y. Meir, A. Stern and N. B. Zhitenev. This work was supported by the Israeli Science Foundation and the German MINERVA foundation.

Author information

Author notes

  1. S. Ilani

    Present address: Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York, 14853, USA

Authors and Affiliations

  1. Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel

    S. Ilani, J. Martin, E. Teitelbaum, D. Mahalu, V. Umansky & A. Yacoby

  2. Max-Planck-Institut für Festkörperforschung, Stuttgart, D-70569, Germany

    J. H. Smet

Authors
  1. S. Ilani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. E. Teitelbaum
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. J. H. Smet
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. D. Mahalu
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. V. Umansky
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. A. Yacoby
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. Ilani.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ilani, S., Martin, J., Teitelbaum, E. et al. The microscopic nature of localization in the quantum Hall effect. Nature 427, 328–332 (2004). https://doi.org/10.1038/nature02230

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature02230

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing