Abstract
The competition between superconductivity and localization raises profound questions in condensed-matter physics. In spite of decades of research, the mechanism of the superconductor–insulator transition and the nature of the insulator are not understood. We use quantum Monte Carlo simulations that treat, on an equal footing, inhomogeneous amplitude variations and phase fluctuations, a major advance over previous theories. We gain new microscopic insights and make testable predictions for local spectroscopic probes. The energy gap in the density of states survives across the transition, but coherence peaks exist only in the superconductor. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has a two-particle gap scale that vanishes at the superconductor–insulator transition, despite a robust single-particle gap.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 12 print issues and online access
$209.00 per year
only $17.42 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
Goldman, A. & Markovic, N. Superconductor–insulator transitions in the two-dimensional limit. Phys. Today 51, 39–44 (November, 1998).
Gantmakher, V. F. & Dolgopolov, V. T. Superconductor–insulator quantum phase transition. Phys. Usp. 53, 3–53 (2010).
Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).
Hebard, A. F. & Paalanen, M. A. Magnetic-field-tuned superconductor–insulator transition in two-dimensional films. Phys. Rev. Lett. 65, 927–930 (1990).
Shahar, D. & Ovadyahu, Z. Superconductivity near the mobility edge. Phys. Rev. B 46, 10917–10922 (1992).
Adams, P. W. Field-induced spin mixing in ultra-thin superconducting Al and Be films in high parallel magnetic fields. Phys. Rev. Lett. 92, 067003 (2004).
Steiner, M. A., Boebinger, G. & Kapitulnik, A. Possible field-tuned superconductor–insulator transition in high- T c superconductors: Implications for pairing at high magnetic fields. Phys. Rev. Lett. 94, 107008 (2005).
Stewart, M. D., Yin, A., Xu, J. M. & Valles, J. M. Superconducting pair correlations in an amorphous insulating nanohoneycomb film. Science 318, 1273–1275 (2007).
Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).
Anderson, P. W. Theory of dirty superconductors. J. Phys. Chem. Solids 11, 26–30 (1959).
Abrikosov, A. A. & Gor’kov, L. P. Superconducting alloys at finite temperatures. Zh. Eksp. Teor. Fiz. 36, 319–320 (1959) (English translation in Sov. Phys. J. Exp. Theoret. Phys. 9, 220–221 (1959)).
Ma, M. & Lee, P. A. Localized superconductors. Phys. Rev. B 32, 5658–5667 (1985).
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).
Ghosal, A., Randeria, M. & Trivedi, N. Role of spatial amplitude fluctuations in highly disordered s-wave superconductors. Phys. Rev. Lett. 81, 3940–3943 (1998).
Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).
Feigel’man, M. V., Ioffe, L. B., Kravtsov, V. E. & Yuzbashyan, E. A. Eigenfunction fractality and pseudogap state near the superconductor–insulator transition. Phys. Rev. Lett. 98, 027001 (2007).
Dubi, Y., Meir, Y. & Avishai, Y. Nature of the superconductor–insulator transition in disordered superconductors. Nature 449, 876–880 (2007).
Sacépé, B., Chapelier, C., Baturina, T. I., Vinokur, V. M., Baklanov, M. R. & Sanquer, M. Disorder-induced inhomogeneities of the superconducting state close to the superconductor–insulator transition. Phys. Rev. Lett. 101, 157006 (2008).
Cren, T., Roditchev, D., Sacks, W., Klein, J., Moussy, J-B., Deville-Cavellin, C. & Laguës, M. Influence of disorder on the local density of states in high- T c superconducting thin films. Phys. Rev. Lett. 84, 147–150 (2000).
Lang, K. M. et al. Imaging the granular structure of high- T c superconductivity in underdoped Bi2Sr2CaCu2O8+δ . Nature 415, 412–416 (2002).
Gomes, K., Pasupathy, A. N., Pushp, A., Ono, S., Ando, Y. & Yazdani, A. Visualizing pair formation on the atomic scale in the high- T c superconductor Bi2Sr2CaCu2O8+δ . Nature 447, 569–572 (2007).
Crane, R. W., Armitage, N. P., Johansson, A., Sambandamurthy, G., Shahar, D. & Grüner, G. Fluctuations, dissipation, and nonuniversal superfluid jumps in two-dimensional superconductors. Phys. Rev. B 75, 094506 (2007).
Blankenbecler, R., Scalapino, D. J. & Sugar, R. L. Monte Carlo calculations of coupled boson-fermion systems. I. Phys. Rev. D 24, 2278–2286 (1981).
Gubernatis, J. E., Jarrell, M., Silver, R. N. & Sivia, D. S. Quantum Monte Carlo simulations and maximum entropy: Dynamics from imaginary-time data. Phys. Rev. B 44, 6011–6029 (1991).
Sandvik, A. W. Stochastic method for analytic continuation of quantum Monte Carlo data. Phys. Rev. B 57, 10287–10290 (1998).
Scalapino, D. J., White, S. R. & Zhang, S. Insulator, metal, or superconductor: The criteria. Phys. Rev. B 47, 7995–8007 (1993).
Trivedi, N., Scalettar, R. T. & Randeria, M. Superconductor–insulator transition in a disordered electronic system. Phys. Rev. B 54, R3756–R3759 (1996).
Fisher, M. P. A., Weichman, P. B., Grinstein, G. & Fisher, D. S. Boson localization and the superfluid-insulator transition. Phys. Rev. B 40, 546–570 (1989).
Finkel’stein, A. M. Suppression of superconductivity in homogenously disordered systems. Physica B 197, 636–648 (1994).
Emery, V. J. & Kivelson, S. A. Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).
Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nature Phys. 7, 239–244 (2011).
Sacépé, B. et al. Pseudogap in a thin film of a conventional superconductor. Nature Commun. 1, 140 (2010).
Mondal, M. et al. Phase fluctuations in a strongly disordered s-wave NbN superconductor close to the metal–insulator transition. Phys. Rev. Lett. 106, 047001 (2011).
Hetel, I., Lemberger, T. R. & Randeria, M. Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin copper oxide films. Nature Phys. 3, 700–702 (2007).
Acknowledgements
We gratefully acknowledge support from NSF DMR-0907275 (K.B.), US Department of Energy, Office of Basic Energy Sciences grant DOE DE-FG02-07ER46423 (N.T., Y.L.L.), NSF DMR-0706203 and NSF DMR-1006532 (M.R.), and computational support from the Ohio Supercomputing Center.
Author information
Authors and Affiliations
Contributions
K.B. and Y.L.L. performed the numerical calculations; M.R. and N.T. were responsible for the project planning; all authors contributed to the data analysis, discussions and writing.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Information (PDF 903 kb)
Rights and permissions
About this article
Cite this article
Bouadim, K., Loh, Y., Randeria, M. et al. Single- and two-particle energy gaps across the disorder-driven superconductor–insulator transition. Nature Phys 7, 884–889 (2011). https://doi.org/10.1038/nphys2037
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1038/nphys2037
This article is cited by
-
Puddle formation and persistent gaps across the non-mean-field breakdown of superconductivity in overdoped (Pb,Bi)2Sr2CuO6+δ
Nature Materials (2023)
-
Field-induced quantum breakdown of superconductivity in magnesium diboride
NPG Asia Materials (2021)
-
Universal behavior of the bosonic metallic ground state in a two-dimensional superconductor
npj Quantum Materials (2021)
-
Overactivated transport in the localized phase of the superconductor-insulator transition
Nature Communications (2021)
-
Quantum breakdown of superconductivity in low-dimensional materials
Nature Physics (2020)