# Pair-breaking quantum phase transition in superconducting nanowires

## Abstract

Quantum phase transitions (QPT) between distinct ground states of matter are widespread phenomena1,2,3,4,5, yet there are only a few experimentally accessible systems6,7 where the microscopic mechanism of the transition can be tested and understood. These cases are unique and form the experimentally established foundation for our understanding of quantum critical phenomena. Here we report that a magnetic-field-driven QPT in superconducting nanowires—a prototypical one-dimensional system (d=1)—can be fully explained by the critical theory8,9 of pair-breaking transitions characterized by a correlation length exponent v≈1 and dynamic critical exponent z≈2. We find that in the quantum critical regime, the electrical conductivity is in agreement with a theoretically predicted scaling function and, moreover, that the theory quantitatively describes the dependence of conductivity on the critical temperature, field magnitude and orientation, nanowire cross-sectional area, and microscopic parameters of the nanowire material. At the critical field, the conductivity follows a T(d–2)/z dependence predicted by phenomenological scaling theories10,11 and more recently obtained within a holographic framework12. Our work uncovers the microscopic processes governing the transition: the pair-breaking effect of the magnetic field on interacting Cooper pairs overdamped by their coupling to electronic degrees of freedom. It also reveals the universal character of continuous quantum phase transitions.

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## Change history

• ### 18 July 2018

In the version of this Letter originally published, one of the authors’ first names was incorrectly spelled Fédéric; it should have read Frédéric. This has now been corrected.

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## Acknowledgements

The authors thank N. Shah, B. Rosenow, S. Sachdev and O. Starykh for valuable comments. Nanowire fabrication was carried out at the University of Utah Microfab and USTAR facilities. A.R. acknowledges Université Grenoble Alpes and Institute Néel, where measurements were performed, for hospitality. This research was supported in part by the National Science Foundation under award numbers DMR-1611421 (A.R.) and DMR-1553991 (A.D.) and by the ERC Grant QUEST number 637815 (B.S.). A.D. performed a portion of this work at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611.

## Author information

Authors

### Contributions

H.K. fabricated nanowires, A.R., B.S. and F.G. carried out measurements, A.R., B.S. and A.D. carried out data analysis and wrote the manuscript, A.R. conceived and coordinated the project.

### Corresponding author

Correspondence to Andrey Rogachev.

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## Supplementary information

### Supplementary Information

2 Tables, 1 Figure, 11 References

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Reprints and Permissions

Kim, H., Gay, F., Del Maestro, A. et al. Pair-breaking quantum phase transition in superconducting nanowires. Nature Phys 14, 912–917 (2018). https://doi.org/10.1038/s41567-018-0179-8

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