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Collective energy gap of preformed Cooper pairs in disordered superconductors


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.

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.


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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



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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The authors declare no competing interests.

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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).

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