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Single- and two-particle energy gaps across the disorder-driven superconductor–insulator transition

Nature Physics volume 7, pages 884–889 (2011)Cite this article

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.

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Figure 1: Energy and temperature scales across SIT.
Figure 2: The single-particle DOS.
Figure 3: Imaginary part of the dynamical pair susceptibility.
Figure 4: Local density of states (LDOS) N(R,ω), density n(R), and BdG pairing amplitude Δop(R) as a function of disorder strength for a montage of nine disorder realizations of 8×8lattices.
Figure 5: Emergent granularity.

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References

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

    Article  Google Scholar 

  2. Gantmakher, V. F. & Dolgopolov, V. T. Superconductor–insulator quantum phase transition. Phys. Usp. 53, 3–53 (2010).

    Article  ADS  Google Scholar 

  3. Haviland, D. B., Liu, Y. & Goldman, A. M. Onset of superconductivity in the two-dimensional limit. Phys. Rev. Lett. 62, 2180–2183 (1989).

    Article  ADS  Google Scholar 

  4. 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  Google Scholar 

  5. Shahar, D. & Ovadyahu, Z. Superconductivity near the mobility edge. Phys. Rev. B 46, 10917–10922 (1992).

    Article  ADS  Google Scholar 

  6. 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).

    Article  ADS  Google Scholar 

  7. 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).

    Article  ADS  Google Scholar 

  8. 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).

    Article  ADS  Google Scholar 

  9. Sachdev, S. Quantum Phase Transitions (Cambridge Univ. Press, 1999).

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. 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)).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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  Google Scholar 

  14. 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  Google Scholar 

  15. Ghosal, A., Randeria, M. & Trivedi, N. Inhomogeneous pairing in highly disordered s-wave superconductors. Phys. Rev. B 65, 014501 (2001).

    Article  ADS  Google Scholar 

  16. 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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. 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).

    Article  ADS  Google Scholar 

  19. 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).

    Article  ADS  Google Scholar 

  20. Lang, K. M. et al. Imaging the granular structure of high- T c superconductivity in underdoped Bi2Sr2CaCu2O8+δ . Nature 415, 412–416 (2002).

    Article  ADS  Google Scholar 

  21. 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).

    Article  ADS  Google Scholar 

  22. 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).

    Article  ADS  Google Scholar 

  23. Blankenbecler, R., Scalapino, D. J. & Sugar, R. L. Monte Carlo calculations of coupled boson-fermion systems. I. Phys. Rev. D 24, 2278–2286 (1981).

    Article  ADS  Google Scholar 

  24. 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).

    Article  ADS  Google Scholar 

  25. Sandvik, A. W. Stochastic method for analytic continuation of quantum Monte Carlo data. Phys. Rev. B 57, 10287–10290 (1998).

    Article  ADS  Google Scholar 

  26. Scalapino, D. J., White, S. R. & Zhang, S. Insulator, metal, or superconductor: The criteria. Phys. Rev. B 47, 7995–8007 (1993).

    Article  ADS  Google Scholar 

  27. Trivedi, N., Scalettar, R. T. & Randeria, M. Superconductor–insulator transition in a disordered electronic system. Phys. Rev. B 54, R3756–R3759 (1996).

    Article  ADS  Google Scholar 

  28. 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).

    Article  ADS  Google Scholar 

  29. Finkel’stein, A. M. Suppression of superconductivity in homogenously disordered systems. Physica B 197, 636–648 (1994).

    Article  ADS  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  Google Scholar 

  31. Sacépé, B. et al. Localization of preformed Cooper pairs in disordered superconductors. Nature Phys. 7, 239–244 (2011).

    Article  ADS  Google Scholar 

  32. Sacépé, B. et al. Pseudogap in a thin film of a conventional superconductor. Nature Commun. 1, 140 (2010).

    Article  Google Scholar 

  33. 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).

    Article  ADS  Google Scholar 

  34. 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).

    Article  ADS  Google Scholar 

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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.

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Authors and Affiliations

  1. Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA

    Karim Bouadim, Yen Lee Loh, Mohit Randeria & Nandini Trivedi

Authors
  1. Karim Bouadim
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  2. Yen Lee Loh
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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.

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Correspondence to Nandini Trivedi.

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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

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