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# Thermodynamic signature of a magnetic-field-driven phase transition within the superconducting state of an underdoped cuprate

## Abstract

More than a quarter century after the discovery of the high-temperature superconductor (HTS) YBa2Cu3O6+δ (YBCO; ref. 1), studies continue to uncover complexity in its phase diagram. In addition to HTS and the pseudogap2,3, there is growing evidence for multiple phases with boundaries which are functions of temperature (T), doping (p) and magnetic field4,5,6,7,8. Here we report the low-temperature electronic specific heat (Celec) of YBa2Cu3O6.43 and YBa2Cu3O6.47 (p = 0.076 and 0.084) up to a magnetic field (H) of 34.5 T, a poorly understood region of the underdoped HTp phase space. We observe two regimes in the low-temperature limit: below a characteristic magnetic field H′ ≈ 12–15 T, Celec/T obeys an expected H1/2 behaviour9,10; however, near H′ there is a sharp inflection followed by a linear-in-H behaviour. H′ rests deep within the superconducting phase and, thus, the linear-in-H behaviour is observed in the zero-resistance regime11. In the limit of zero temperature, Celec/T is proportional to the zero-energy electronic density of states. At one of our dopings, the inflection is sharp only at lowest temperatures, and we thus conclude that this inflection is evidence of a magnetic-field-driven quantum phase transition.

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## Acknowledgements

The authors thank S. Kivelson, R. Baumbach, A. Kapitulnik, M. Norman, B. Ramshaw, A. Shekhter, J. Sonier and S. Riggs for discussions and commentary on the manuscript, as well as A. Migliori for discussions on the experimental techniques. J.B.K. thanks C. Moir for assistance during experiments. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-1157490, the State of Florida, and the US Department of Energy. Work at the University of British Columbia was supported by the Natural Science and Engineering Research Council of Canada and the Canadian Institute for Advanced Research.

## Affiliations

1. ### Department of Physics and National High Magnetic Field Laboratory, Florida State University, Tallahassee, Florida 32310, USA

• J. B. Kemper
• , O. Vafek
•  & G. S. Boebinger
2. ### National High Magnetic Field Laboratory, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

• J. B. Betts
•  & F. F. Balakirev
3. ### Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia V6T 1Z4, Canada

• W. N. Hardy
• , Ruixing Liang
•  & D. A. Bonn
4. ### Canadian Institute for Advanced Research, 180 Dundas Street West, Suite 1400, Toronto, Ontario M5G 1Z8, Canada

• W. N. Hardy
• , Ruixing Liang
•  & D. A. Bonn

## Authors

### Contributions

W.N.H., R.L. and D.A.B. prepared the samples and contributed to the experimental plan. J.B.K. refined the experimental set-up, performed the experiments, analysed the data and contributed to the writing of the manuscript. O.V. contributed to the writing of the manuscript and interpretation of results. G.S.B. supervised the project and contributed to the writing of the manuscript. F.F.B. contributed to the experimental software and thermometer calibrations. J.B.B. contributed to the experimental hardware and thermometer calibrations. F.F.B., J.B.B. and D.A.B. provided comments on the results and manuscript.

### Competing interests

The authors declare no competing financial interests.

## Corresponding author

Correspondence to J. B. Kemper.

## PDF files

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### Supplementary information

Supplementary information

### DOI

https://doi.org/10.1038/nphys3502

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