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Collective energy gap of preformed Cooper pairs in disordered superconductors

Nature Physics volume 15, pages 233–236 (2019)Cite this article

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Abstract

In most superconductors, the transition to the superconducting state is driven by the binding of electrons into Cooper pairs1. The condensation of these pairs into a single, phase-coherent, quantum state takes place at the same time as their formation at the transition temperature, Tc. A different scenario occurs in some disordered, amorphous, superconductors: instead of a pairing-driven transition, incoherent Cooper pairs first preform above Tc, causing the opening of a pseudogap, and then, at Tc, condense into the phase-coherent superconducting state2,3,4,5,6,7,8,9,10,11. Such a two-step scenario implies the existence of a new energy scale, Δc, driving the collective superconducting transition of the preformed pairs2,3,4,5,6. Here we unveil this energy scale by means of Andreev spectroscopy5,12 in superconducting thin films of amorphous indium oxide. We observe two Andreev conductance peaks at ±Δc that develop only below Tc and for highly disordered films on the verge of the transition to insulator. Our findings demonstrate that amorphous superconducting films provide prototypical disordered quantum systems to explore the collective superfluid transition of preformed Cooper pairs.

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Fig. 1: From tunnelling to Andreev spectroscopy.
Fig. 2: Temperature dependence of the Andreev spectroscopy.
Fig. 3: Collective gap versus spectral gap.
Fig. 4: Two-step transition to superconductor.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

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

    Article  MathSciNet  Google Scholar 

  2. 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  Google Scholar 

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

    Article  Google Scholar 

  4. 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  Google Scholar 

  5. Feigel’man, M. V., Ioffe, L. B., Kravtsov, V. E. & Cuevas, E. Fractal superconductivity near localization threshold. Ann. Phys. 325, 1390–1478 (2010).

    Article  Google Scholar 

  6. Bouadim, K., Loh, Y. L., Randeria, M. & Trivedi, N. Single- and two-particle energy gaps across the disorder-driven superconductor-insulator transition. Nat. Phys. 7, 884–889 (2011).

    Article  Google Scholar 

  7. Sacépé, B. et al. Disorder-induced inhomogeneities of the superconducting state close to the superconductor–insulator transition. Phys. Rev. Lett. 101, 157006 (2008).

    Article  Google Scholar 

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

    Article  Google Scholar 

  9. 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  Google Scholar 

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

    Article  Google Scholar 

  11. Chand, M. et al. Phase diagram of the strongly disordered s-wave superconductor NbN close to the metal–insulator transition. Phys. Rev. B 85, 014508 (2012).

    Article  Google Scholar 

  12. Deutscher, G. Andreev–Saint-James reflections: a probe of cuprate superconductors. Rev. Mod. Phys. 77, 109–135 (2005).

    Article  Google Scholar 

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

    Article  Google Scholar 

  14. Abrikosov, A. A. & Gorkov, I. P. On the theory of superconducting alloys. Sov. Phys. JETP 8, 1090–1098 (1959).

    Google Scholar 

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

    Article  Google Scholar 

  16. Gantmakher, V. F. & Dolgopolov, V. T. Superconductor–insulator quantum phase transition. Phys.-Uspekhi 53, 1–49 (2010).

    Article  Google Scholar 

  17. Sherman, D., Kopnov, G., Shahar, D. & Frydman, A. Measurement of a superconducting energy gap in a homogeneously amorphous insulator. Phys. Rev. Lett. 108, 177006 (2012).

    Article  Google Scholar 

  18. Noat, Y. et al. Unconventional superconductivity in ultrathin superconducting NbN films studied by scanning tunneling spectroscopy. Phys. Rev. B 88, 014503 (2013).

    Article  Google Scholar 

  19. Ganguly, R. et al. Magnetic field induced emergent inhomogeneity in a superconducting film with weak and homogeneous disorder. Phys. Rev. B 96, 054509 (2017).

    Article  Google Scholar 

  20. Deutscher, G. Coherence and single-particle excitations in the high-temperature superconductors. Nature 397, 410–412 (1999).

    Article  Google Scholar 

  21. Andreev, A. F. The thermal conductivity of the intermediate state in superconductors. Sov. Phys. JETP 19, 1228–1231 (1964).

    Google Scholar 

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

    Article  Google Scholar 

  23. Agraït, N., Rodrigo, J. G. & Vieira, S. Transition from the tunneling regime to point contact and proximity-induced Josephson effect in lead–normal–metal nanojunctions. Phys. Rev. B 46, (R)5814–(R)5817 (1992).

    Article  Google Scholar 

  24. Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes in superconducting microconstrictions: excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 4515–4532 (1982).

    Article  Google Scholar 

  25. Burmistrov, I. S., Gornyi, I. V. & Mirlin, A. D. Local density of states and its mesoscopic fluctuations near the transition to a superconducting state in disordered systems. Phys. Rev. B 93, 205432 (2016).

    Article  Google Scholar 

  26. Klapwijk, T. M., Blonder, G. E. & Tinkham, M. Explanation of subharmonic energy gap structure in superconducting contacts. Physica 109–110, 1657–1664 (1982).

    Google Scholar 

  27. Octavio, M., Tinkham, M., Blonder, G. E. & Klapwijk, T. M. Subharmonic energy-gap structure in superconducting constrictions. Phys. Rev. B 27, 6739–6746 (1983).

    Article  Google Scholar 

  28. Sacépé, B. et al. High-field termination of a Cooper-pair insulator. Phys. Rev. B 91, 220508(R) (2015).

    Article  Google Scholar 

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Acknowledgements

We thank M. Feigel’man, L. Ioffe and Y. Nazarov for fruitful discussions. This research was supported in part by the French National Agency ANR-10-BLANC-04030-POSTIT, ANR-16-CE30-0019-ELODIS2 and the H2020 ERC grant QUEST no. 637815.

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Authors and Affiliations

  1. Univ. Grenoble Alpes, CEA, INAC, PHELIQS, Grenoble, France

    Thomas Dubouchet, Marc Sanquer & Claude Chapelier

  2. Univ. Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Benjamin Sacépé & Johanna Seidemann

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

    Dan Shahar

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Contributions

B.S. and J.S. prepared the samples. T.D. and C.C. performed the experiments. T.D., B.S. and C.C. carried out the analysis and interpretation of the results. B.S. wrote the manuscript with the input of all co-authors. C.C. conceived and supervised the project.

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Correspondence to Benjamin Sacépé or Claude Chapelier.

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Supplementary Information

Supplementary Figures 1–11; Supplementary Table 1; Supplementary References 1–6

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Dubouchet, T., Sacépé, B., Seidemann, J. et al. Collective energy gap of preformed Cooper pairs in disordered superconductors. Nat. Phys. 15, 233–236 (2019). https://doi.org/10.1038/s41567-018-0365-8

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