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# Universal T-linear resistivity and Planckian dissipation in overdoped cuprates

## Abstract

The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point1,2,3,4 is a major puzzle of condensed-matter physics5. Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bilayer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6−xNd0.4SrxCuO4 (ref. 7) and La2−xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO2 plane), A1, is given by the universal relation A1TF = h/2e2, where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1/τ of charge carriers reaches the Planckian limit9,10, whereby ħ/τ = kBT, works not only for hole-doped cuprates6,7,8,11,12 but also for electron-doped cuprates13,14, despite the different nature of their quantum critical point and strength of their electron correlations.

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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 authors (L.T. or C.P.) upon reasonable request.

## References

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## Acknowledgements

The authors would like to thank K. Behnia, C. Bourbonnais, R. Greene, S. Hartnoll, N. Hussey, M.-H. Julien, D. Maslov, J. Paglione, S. Sachdev, A.-M. Tremblay and J. Zaanen for fruitful discussions. A portion of this work was performed at the LNCMI, a member of the European Magnetic Field Laboratory (EMFL). C.P. acknowledges funding from the French ANR SUPERFIELD, and the LABEX NEXT. P.F. and L.T. acknowledge support from the Canadian Institute for Advanced Research (CIFAR) and funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Fonds de recherche du Québec - Nature et Technologies (FRQNT) and the Canada Foundation for Innovation (CFI). L.T. acknowledges support from a Canada Research Chair. This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund. Part of this work was funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant GBMF5306 to L.T.).

## Author information

Authors

### Contributions

A.L., S.B., W.T., B.V., D.V. and C.P. performed the transport measurements at the LNCMI. A.L., F.L., M.L. and N.D.-L. performed the transport measurements at Sherbrooke. H.R., P.A.-S. and Z.Z.L. prepared the Bi2212 film, which was then characterized by A.L., H.R., P.A.-S., Z.Z.L. and D.C. M.D. and P.F. prepared and characterized the PCCO films. A.L., F.L., L.T. and C.P. wrote the manuscript, in consultation with all authors. L.T. and C.P. co-supervised the project.

### Corresponding authors

Correspondence to L. Taillefer or C. Proust.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

10 Figures, 4 Tables, 11 References

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Reprints and Permissions

Legros, A., Benhabib, S., Tabis, W. et al. Universal T-linear resistivity and Planckian dissipation in overdoped cuprates. Nature Phys 15, 142–147 (2019). https://doi.org/10.1038/s41567-018-0334-2

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• DOI: https://doi.org/10.1038/s41567-018-0334-2

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