Skip to main content

Thank you for visiting 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.

Nature of the superconductor–insulator transition in disordered superconductors


The interplay of superconductivity and disorder has intrigued scientists for several decades. Disorder is expected to enhance the electrical resistance of a system, whereas superconductivity is associated with a zero-resistance state. Although superconductivity has been predicted to persist even in the presence of disorder1, experiments performed on thin films have demonstrated a transition from a superconducting to an insulating state with increasing disorder or magnetic field2. The nature of this transition is still under debate, and the subject has become even more relevant with the realization that high-transition-temperature (high-Tc) superconductors are intrinsically disordered3,4,5. Here we present numerical simulations of the superconductor–insulator transition in two-dimensional disordered superconductors, starting from a microscopic description that includes thermal phase fluctuations. We demonstrate explicitly that disorder leads to the formation of islands where the superconducting order is high. For weak disorder, or high electron density, increasing the magnetic field results in the eventual vanishing of the amplitude of the superconducting order parameter, thereby forming an insulating state. On the other hand, at lower electron densities or higher disorder, increasing the magnetic field suppresses the correlations between the phases of the superconducting order parameter in different islands, giving rise to a different type of superconductor–insulator transition. One of the important predictions of this work is that in the regime of high disorder, there are still superconducting islands in the sample, even on the insulating side of the transition. This result, which is consistent with experiments6,7, explains the recently observed huge magneto-resistance peak in disordered thin films8,9,10 and may be relevant to the observation of ‘the pseudogap phenomenon’ in underdoped high-Tc superconductors11,12.

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

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


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

Figure 1: Spatial fluctuations of the order parameter amplitude and corresponding phase correlations.
Figure 2: The superconductor–insulator phase transition with amplitude vanishing and loss of phase coherence.
Figure 3: Superconducting islands observed by phase correlations and by application of a parallel field.


  1. Anderson, P. W. Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26–30 (1959)

    Article  ADS  CAS  Google Scholar 

  2. Goldman, A. M. & Markovic, N. Superconductor-insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (1998)

    Article  CAS  Google Scholar 

  3. Reich, S. et al. Localized high-Tc superconductivity on the surface of Na-doped WO 3. J. Superconductivity 13, 855–861 (2000)

    Article  ADS  CAS  Google Scholar 

  4. Cren, T., Roditchev, D., Sacks, W. & Klein, J. Nanometer scale mapping of the density of states in an inhomogeneous superconductor. Europhys. Lett. 54, 84–90 (2001)

    Article  ADS  CAS  Google Scholar 

  5. Pan, S. H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x . Nature 413, 282–285 (2001)

    Article  ADS  CAS  Google Scholar 

  6. Kowal, D. & Ovadyahu, Z. Disorder induced granularity in an amorphous superconductor. Solid State Commun. 90, 783–786 (1994)

    Article  ADS  CAS  Google Scholar 

  7. Crane, R. W. et al. Survival of superconducting correlations across the two-dimensional superconductor-insulator transition: A finite-frequency study. Phys. Rev. B 75, 184530 (2007)

    Article  ADS  Google Scholar 

  8. Paalanen, M. A., Hebard, A. F. & Ruel, R. R. Low-temperature insulating phases of uniformly disordered two-dimensional superconductors. Phys. Rev. Lett. 69, 1604–1607 (1992)

    Article  ADS  CAS  Google Scholar 

  9. Gantmakher, V. F., Golubkov, M. V., Lok, J. G. S. & Geim, A. K. Giant negative magnetoresistance of semi-insulating amorphous indium oxide films in strong magnetic fields. J. Exp. Theor. Phys. 82, 951–958 (1996)

    ADS  Google Scholar 

  10. Sambandamurthy, G., Engel, L. W., Johansson, A. & Shahar, D. Superconductivity-related insulating behavior. Phys. Rev. Lett. 92, 107005 (2004)

    Article  ADS  CAS  Google Scholar 

  11. Timusk, T. & Statt, B. The pseudogap in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 62, 61–122 (1999)

    Article  ADS  CAS  Google Scholar 

  12. Alvarez, G., Mayr, M., Moreo, A. & Dagotto, E. Areas of superconductivity and giant proximity effects in underdoped cuprates. Phys. Rev. B 71, 014514 (2005)

    Article  ADS  Google Scholar 

  13. Bardeen, J., Cooper, L. N. & Schrieffer, J. R. Theory of superconductivity. Phys. Rev. 108, 1175–1204 (1957)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  14. Ma, M. & Lee, P. A. Localized superconductors. Phys. Rev. B 32, 5658–5667 (1985)

    Article  ADS  CAS  Google Scholar 

  15. Fisher, M. P. A., Grinstein, G. & Girvin, S. M. Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition. Phys. Rev. Lett. 64, 587–590 (1990)

    Article  ADS  CAS  Google Scholar 

  16. Fisher, M. P. A. Quantum phase transitions in disordered two-dimensional superconductors. Phys. Rev. Lett. 65, 923–926 (1990)

    Article  ADS  CAS  Google Scholar 

  17. Galitski, V. M. & Larkin, A. I. Disorder and quantum fluctuations in superconducting films in strong magnetic fields. Phys. Rev. Lett. 87, 087001 (2001)

    Article  ADS  CAS  Google Scholar 

  18. Ghosal, A., Randeria, M. & Trivedi, N. Role of spatial amplitude fluctuations in highly disordered s-wave superconductors. Phys. Rev. Lett. 81, 3940–3943 (1998)

    Article  ADS  CAS  Google Scholar 

  19. De-Gennes, P. G. Superconductivity of Metals and Alloys (W. A. Benjamin, New York, 1966)

    MATH  Google Scholar 

  20. Mayr, M., Alvarez, G., Sen, C. & Dagotto, E. Phase fluctuations in strongly coupled d-wave superconductors. Phys. Rev. Lett. 94, 217001 (2005)

    Article  ADS  Google Scholar 

  21. Dubi, Y., Meir, Y. & Avishai, Y. Theory of magneto-resistance in disordered superconducting films. Phys. Rev. B 73, 054509 (2006)

    Article  ADS  Google Scholar 

  22. Clogston, A. M. Upper limit for the critical field in hard superconductors. Phys. Rev. Lett. 9, 266–267 (1962)

    Article  ADS  Google Scholar 

  23. Chandrasekhar, B. S. A note on the maximum critical field of high-field superconductors. Appl. Phys. Lett. 1, 7–8 (1962)

    Article  ADS  CAS  Google Scholar 

  24. Ephron, D., Yazdani, A., Kapitulnik, A. & Beasley, M. R. Observation of quantum dissipation in the vortex state of a highly disordered superconducting thin film. Phys. Rev. Lett. 76, 1529–1532 (1996)

    Article  ADS  CAS  Google Scholar 

  25. Aubin, H. et al. Magnetic-field-induced quantum superconductor-insulator transition in Nb0. 15Si0. 85 . Phys. Rev. B 73, 094521 (2006)

    Article  ADS  Google Scholar 

  26. Hebard, A. F. & Paalanen, M. A. Magnetic-field-tuned superconductor-insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990)

    Article  ADS  CAS  Google Scholar 

  27. Yazdani, A. & Kapitulnik, A. Superconducting-insulating transition in two-dimensional a-MoGe thin films. Phys. Rev. Lett. 74, 3037–3040 (1995)

    Article  ADS  CAS  Google Scholar 

  28. Das Gupta, K., Sambandamurthy, G., Soman, S. S. & Chandrasekhar, N. Possible robust insulator-superconductor transition on solid inert gas and other substrates. Phys. Rev. B 63, 104502 (2001)

    Article  ADS  Google Scholar 

  29. Baturina, T. I. et al. Superconductivity on the localization threshold and magnetic-field-tuned superconductor-insulator transition in TiN films. JETP Lett. 79, 337–341 (2004)

    Article  ADS  CAS  Google Scholar 

  30. Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995)

    Article  ADS  CAS  Google Scholar 

Download references


We acknowledge discussions with A. Auerbach. This work was carried out with the support of the Israel Science Foundation and the US-Israel Binational Science Foundation. Y.D. acknowledges support from a Kreitman fellowship. Y.M. acknowledges the hospitality of the Aspen Center of Physics. Y.A. acknowledges JSPS fellowship.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Yigal Meir.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor–insulator transition in disordered superconductors. Nature 449, 876–880 (2007).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

This article is cited by


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.


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