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# Low-temperature anomaly in disordered superconductors near Bc2 as a vortex-glass property

## Abstract

Strongly disordered superconductors in a magnetic field exhibit many characteristic properties of type-II superconductivity—except at low temperatures, where an anomalous linear temperature dependence of the resistive critical field Bc2 is routinely observed. This behaviour violates the conventional theory of superconductivity, and its origin has posed a long-standing puzzle. Here we report systematic measurements of the critical magnetic field and current on amorphous indium oxide films with various levels of disorder. Surprisingly, our measurements show that the Bc2 anomaly is accompanied by mean-field-like scaling of the critical current. Based on a comprehensive theoretical study we argue that these observations are a consequence of the vortex-glass ground state and its thermal fluctuations. Our theory further predicts that the linear-temperature anomaly occurs more generally in both films and disordered bulk superconductors, with a slope that depends on the normal-state sheet resistance, which we confirm experimentally.

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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.

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## Change history

• ### 30 October 2018

In the version of this Article originally published, equation (5) was incorrect; see the correction notice for details. This has been corrected in all versions of the Article.

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## Acknowledgements

We are grateful to V. Geshkenbein, L. Ioffe, T. Klein and M. Skvortsov for useful discussions. We thank I. Tamir and D. Shahar for providing sample ITb1. B.S., J.S. and F.G. acknowledge support from the LANEF framework (ANR-10-LABX-51-01) and the H2020 ERC grant QUEST no. 637815. K.D. and A.R. acknowledge support from NSF grant no. DMR 1611421. The research of K.M was supported by the Israel Science Foundation grant no. 1889/16. The research of M.V.F. was partially supported by a Skoltech NGP grant.

## Author information

### Affiliations

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

• Benjamin Sacépé
• , Johanna Seidemann
•  & Frédéric Gay
2. #### Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, USA

• Kevin Davenport
•  & Andrey Rogachev
3. #### Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot, Israel

•  & Karen Michaeli
4. #### L. D. Landau Institute for Theoretical Physics, Chernogolovka, Russia

• Mikhail V. Feigel’man
5. #### Skolkovo Institute of Science and Technology, Moscow, Russia

• Mikhail V. Feigel’man

### Contributions

J.S., K.D., A.R. and B.S. fabricated the samples. F.G. provided technical support for low-temperature set-ups and measurements. B.S., J.S. and M.O. performed the measurements. B.S. and J.S. carried out data analysis. K.M. and M.F. developed the theory. B.S., K.M and M.F. wrote the manuscript. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing interests.

### Corresponding author

Correspondence to Benjamin Sacépé.

## Supplementary information

1. ### Supplementary Information

14 pages, 9 figures, 1 table, 16 references