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First-order quantum breakdown of superconductivity in an amorphous superconductor

Nature Physics volume 21, pages 104–109 (2025)Cite this article

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Abstract

Continuous quantum phase transitions are widely assumed and frequently observed in various systems of quantum particles or spins. Their characteristic trait is a second-order, gradual suppression of the order parameter as the quantum critical point is approached. The localization of Cooper pairs in disordered superconductors and the resulting breakdown of superconductivity have long stood as a prototypical example. Here we show a departure from this paradigm, in which a discontinuous first-order quantum phase transition is tuned by disorder. We measure the plasmon spectrum in superconducting microwave resonators on amorphous superconducting films of indium oxide to provide evidence for a marked jump in both the zero-temperature superfluid stiffness and the transition temperature at the critical disorder. This discontinuous transition sheds light on the role of repulsive interactions between Cooper pairs and the subsequent competition between superconductivity and insulating Cooper-pair glass. Furthermore, we show that the critical temperature of the films no longer relates to the pairing amplitude but aligns with the superfluid stiffness, consistent with the pseudogap regime of preformed Cooper pairs. Our findings raise fundamental new questions about the role of disorder in quantum phase transitions and carry implications for superinductances in quantum circuits.

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Fig. 1: Resistivity and microwave spectroscopy of indium oxide striplines.
Fig. 2: Phase-driven superconducting transition.
Fig. 3: First-order quantum breakdown of superconductivity.

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Source data are provided with this paper. All other 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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Acknowledgements

We thank D. Basko, L. Benfatto, J. Delahaye, T. Grenet, V. Kravtsov, M. Müller, M. Scheffler and C. Strunk for valuable discussions. We thank É. Eyraud for assistance with the cryogenics and J. P. Martinez for the preliminary measurements. T.C. and B.S. acknowledge funding from the ANR Project No. ANR-19-CE30-0014-CP-Insulators. A.K. is grateful for support from the Laboratoire d’excellence LANEF in Grenoble (ANR-10-LABX-51-01). B.S. has received funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant SUPERGRAPH no. 866365. N.R. has received funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant SuperProtected no. 101001310. N.R., B.S. and D.P. acknowledge funding from the ANR agency under the ‘France 2030’ plan, with reference no. ANR-22-PETQ-0003. I.P. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) via grant no. MI 658/14-1.

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Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Thibault Charpentier, David Perconte, Sébastien Léger, Kazi Rafsanjani Amin, Florent Blondelle, Frédéric Gay, Olivier Buisson, Nicolas Roch & Benjamin Sacépé

  2. Google Research, Mountain View, CA, USA

    Lev Ioffe

  3. LPMMC, Université Grenoble Alpes, Grenoble, France

    Anton Khvalyuk & Mikhail Feigel’man

  4. Karlsruhe Institute of Technology, Karlsruhe, Germany

    Igor Poboiko

  5. CENN Nanocenter, Ljubljana, Slovenia

    Mikhail Feigel’man

  6. Jožef Stefan Institute, Ljubljana, Slovenia

    Mikhail Feigel’man

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  1. Thibault Charpentier
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Contributions

T.C. designed the samples. T.C., D.P. and S.L. fabricated the samples. T.C., S.L., K.R.A., F.B. and F.G. worked on the measurement setup. T.C. and D.P. performed the measurements with initial help from S.L. T.C., B.S. and N.R. analysed the data. M.F., I.P., L.I. and A.K. developed the theory and contributed to the data analysis. B.S. and N.R. conceived the project and supervised it with O.B. B.S., T.C. and A.K. wrote the paper with inputs from all co-authors.

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Correspondence to Benjamin Sacépé.

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Extended data

Extended Data Fig. 1 Evolution of superfluid stiffness with critical temperature for various superconductors.

Upon variation of disorder, carrier density or doping, superconductors display a decrease of both superfluid stiffness and critical temperatures. For very low superfluid densities these two quantities become of the same order, as evidenced by the dashed line representing the equality Θ = Tc. a:InO lies on this line in a large disorder range. Data from11,61,67 (NbN),20,51 (grAl),21,68 (LaAlO3/SrTiO3),69 (KTaO3),15,70,71 (MoGe),66 (TiN),38,72 (YBCO). Previous works on a:InO73 and In/a:InO composites71,74 are also added.

Extended Data Fig. 2 Berezinskii-Kosterlitz-Thouless transition of sample DP-Res11.

Left axis displays the superfluid stiffness versus temperature obtained from the T-dependence of the frequency shift of plasma modes via Θ(T) = Θ(0)(f(T)/f(0))2. Dashed red line represents the Berezinskii-Kosterlitz-Thouless universal critical line Θ(T) = 2/πT. Both curves cross exactly at the vortex unbinding temperature TBKT = 0.75 K. Right-axis shows the corresponding superconducting transition in the sheet resistance versus temperature. The dashed orange line illustrates our definition of Tc as a linear extrapolation of the resistance curve, giving Tc = 0.94 K.

Extended Data Fig. 3 Superinductance.

Wave impedance \(Z=\sqrt{l/{c}_{1}}\) versus sheet resistance. The impedance is normalized by h/4e2. All data points lie well above the line Z/(h/4e2) = 1/3, and some of them even achieve Z>h/4e2. This classifies them as superinductances.

Extended Data Fig. 4 Microwave dissipation in a:InO superconducting resonators.

a Evolution of a:InO resonators quality factors upon increasing power for three different sample environments, with varying sensitivity to surface dielectric loss. We studied resonators in the microstrip geometry (see Fig. 1) or embedded in 3D aluminum waveguides (see Fig. S3) with reduced surface loss participation ratio. A third type of sample is capped in-situ after a:InO deposition by a thin aluminum layer to replace the surface dissipation of a:InO by thin aluminum oxide. b Temperature evolution of an a:InO resonator (sample TC040) in 3D waveguide showing non-monotonous behavior. Solid lines in panels a and b are fits following a TLS model (see SI). c Evolution of the low-power, low-temperature quality factor with sheet resistance, for the samples reported in Extended Table I. Near the transition to insulator the quality factor remains >2 × 103. d Evolution of low-power and low-temperature quality factor with metal-substrate participation ratio (see SI). Full symbols correspond to resonators and transmon qubits in a 2D geometry (Ta75, Al and grAl59, TiN66, Al transmons76, a:InO), empty symbols show resonators measured in a 3D waveguide (grAl59, TiN66 and a:InO sample TC040). Dashed lines show the expected scaling for dielectric loss Qi = \({[{{\rm{p}}}_{{\rm{MS}}}\tan \delta ]}^{-1}\) for three values of \(\tan \delta\).

Extended Data Table 1 Summary of experimental data discussed in the text
Full size table

Supplementary information

Supplementary Information

Supplementary Sections I–VI and Figs. 1–4.

Source data

Source Data Fig. 1

Statistical source data for Fig. 1a,d,e.

Source Data Fig. 2

Statistical source data for Fig. 2.

Source Data Fig. 3

Statistical source data for Fig. 3a.

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Charpentier, T., Perconte, D., Léger, S. et al. First-order quantum breakdown of superconductivity in an amorphous superconductor. Nat. Phys. 21, 104–109 (2025). https://doi.org/10.1038/s41567-024-02713-8

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