Universal T-linear resistivity and Planckian dissipation in overdoped cuprates


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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: T-linear resistivity in five overdoped cuprates.
Fig. 2: Resistivity and Hall coefficient of our Bi2212 film.
Fig. 3: Effective mass m* and slope of T-linear resistivity A1 versus p in hole-doped cuprates.
Fig. 4: Effective mass m* and slope of T-linear resistivity A1 versus x in electron-doped cuprates.

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.


  1. 1.

    Löhneysen, H. v. et al. Non-Fermi-liquid behavior in a heavy-fermion alloy at a magnetic instability. Phys. Rev. Lett. 72, 3262–3265 (1994).

    ADS  Article  Google Scholar 

  2. 2.

    Fournier, P. et al. Insulator–metal crossover near optimal doping in Pr2−xCexCuO4: Anomalous normal-state low temperature resistivity. Phys. Rev. Lett. 81, 4720–4723 (1998).

    ADS  Article  Google Scholar 

  3. 3.

    Grigera, S. A. et al. Magnetic field-tuned quantum criticality in the metallic ruthenate Sr3Ru2CuO7. Science 294, 329–332 (2001).

    ADS  Article  Google Scholar 

  4. 4.

    Doiron-Leyraud, N. et al. Correlation between linear resistivity and T c in the Bechgaard salts and the pnictide superconductor Ba(Fe1 xCox)2As2. Phys. Rev. B 80, 214531 (2009).

    ADS  Article  Google Scholar 

  5. 5.

    Coleman, P. & Schofield, A. J. Quantum criticality. Nature 433, 226–229 (2005).

    ADS  Article  Google Scholar 

  6. 6.

    Martin, S. et al. Normal-state transport properties of Bi2+xSr2−yCuO6+δ single crystals. Phys. Rev. B 41, 846–849 (1990).

    ADS  Article  Google Scholar 

  7. 7.

    Daou, R. et al. Linear temperature dependence of resistivity and change in the Fermi surface at the pseudogap critical point of a high-T c superconductor. Nat. Phys. 5, 31–34 (2009).

    Article  Google Scholar 

  8. 8.

    Cooper, R. A. et al. Anomalous criticality in the electrical resistivity of La2−xSrxCuO4. Science 323, 603–607 (2009).

    ADS  Article  Google Scholar 

  9. 9.

    Zaanen, J. Why the temperature is high. Nature 430, 512–513 (2004).

    ADS  Article  Google Scholar 

  10. 10.

    Bruin, J. A. N. et al. Similarity of scattering rates in metals showing T-linear resistivity. Science 339, 804–807 (2013).

    ADS  Article  Google Scholar 

  11. 11.

    Collignon, C. et al. Fermi-surface transformation across the pseudogap critical point of the cuprate superconductor La1.6−xNd0.4SrxCuO4. Phys. Rev. B 95, 224517 (2017).

    ADS  Article  Google Scholar 

  12. 12.

    Doiron-Leyraud, N. et al. Pseudogap phase of cuprate superconductors confined by Fermi surface topology. Nat. Commun. 8, 2044 (2017).

    ADS  Article  Google Scholar 

  13. 13.

    Jin, K. et al. Link between spin fluctuations and electron pairing in copper oxide superconductors. Nature 476, 73–75 (2011).

    Article  Google Scholar 

  14. 14.

    Sarkar, T. et al. Fermi surface reconstruction and anomalous low-temperature resistivity in electron-doped La2 xCexCuO4. Phys. Rev. B 96, 155449 (2017).

    ADS  Article  Google Scholar 

  15. 15.

    Löhneysen, H. v. et al. Fermi-liquid instabilities at magnetic quantum phase transitions. Rev. Mod. Phys. 79, 1015–1075 (2007).

    ADS  Article  Google Scholar 

  16. 16.

    Dagan, Y. et al. Evidence for a quantum phase transition in Pr2 xCexCuO4 from transport measurements. Phys. Rev. Lett. 92, 167001 (2004).

    ADS  Article  Google Scholar 

  17. 17.

    Tafti, F. F. et al. Nernst effect in the electron-doped cuprate superconductor Pr2 xCexCuO4: superconducting fluctuations, upper critical field H c2, and the origin of the T c dome. Phys. Rev. B 90, 024519 (2014).

    ADS  Article  Google Scholar 

  18. 18.

    Motoyama, E. M. et al. Spin correlations in the electron-doped high-transition-temperature superconductor Nd2-xCexCuO4. Nature 445, 186–189 (2007).

    ADS  Article  Google Scholar 

  19. 19.

    Matt, C. E. et al. Electron scattering, charge order, and pseudogap physics in La1.6−xNd0.4SrxCuO4: an angle-resolved photoemission spectroscopy study. Phys. Rev. B 92, 134524 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    Yoshida, T. et al. Systematic doping evolution of the underlying Fermi surface of La2−xSr xCuO4. Phys. Rev. B 74, 224510 (2006).

    ADS  Article  Google Scholar 

  21. 21.

    Kaminski, A. et al. Change of Fermi-surface topology in Bi2Sr2CaCu2O8+δ with doping. Phys. Rev. B 73, 174511 (2006).

    ADS  Article  Google Scholar 

  22. 22.

    Benhabib, S. et al. Collapse of the normal-state pseudogap at a Lifshitz transition in the Bi2Sr2CaCu2O8+δ cuprate superconductor. Phys. Rev. Lett. 114, 147001 (2015).

    ADS  Article  Google Scholar 

  23. 23.

    Hussey, N. E. et al. Phenomenology of the normal-state in-plane transport properties of high-T c cuprates. J. Phys. Condens. Matter 20, 123201 (2008).

    ADS  Article  Google Scholar 

  24. 24.

    Fauqué, B. et al. Dispersion of the odd magnetic resonant mode in near-optimally doped Bi2Sr2CaCu2O8+δ. Phys. Rev. B 76, 214512 (2007).

    ADS  Article  Google Scholar 

  25. 25.

    Tranquada, J. M. et al. Coexistence of, and competition between, superconductivity and charge-stripe order in La1.62−xNd0.4SrxCuO4. Phys. Rev. Lett. 78, 338 (1997).

    ADS  Article  Google Scholar 

  26. 26.

    Hussey, N. E. et al. Generic strange metal behavior of overdoped cuprates. J. Phys. Conf. Series 449, 012004 (2013).

    Article  Google Scholar 

  27. 27.

    Hayes, I. M. et al. Scaling between magnetic field and temperature in the high-temperature superconductor BaFe2(As1−xPx)2. Nat. Phys. 12, 919 (2016).

    Article  Google Scholar 

  28. 28.

    Matsui, H. et al. Evolution of the pseudogap across the magnet–superconductor phase boundary of Nd2−xCexCuO4. Phys. Rev. B 75, 224514 (2007).

    ADS  Article  Google Scholar 

  29. 29.

    Helm, T. et al. Evolution of the Fermi surface of the electron-doped high-temperature superconductor Nd2−xCexCuO4 revealed by Shubnikov–de Haas oscillations. Phys. Rev. Lett. 103, 157002 (2009).

    ADS  Article  Google Scholar 

  30. 30.

    Helm, T. et al. Correlation between Fermi surface transformations and superconductivity in the electron-doped high-T c superconductor Nd2−xCexCuO4. Phys. Rev. B 92, 094501 (2015).

    ADS  Article  Google Scholar 

  31. 31.

    Yu, W. et al. Magnetic-field dependence of the low-temperature specific heat of the electron-doped superconductor Pr1.85Ce0.15CuO4. Phys. Rev. B 72, 212512 (2005).

    ADS  Article  Google Scholar 

  32. 32.

    Bangura, A. et al. Fermi surface and electronic homogeneity of the overdoped cuprate superconductor Tl2Ba2CuO6+δ as revealed by quantum oscillations. Phys. Rev. B. 82, 140501R (2010).

    ADS  Article  Google Scholar 

  33. 33.

    Loram, J. W. et al. Evidence on the pseudogap and the condensate from the electronic specific heat. J. Phys. Chem. Solids 62, 59–64 (2001).

    ADS  Article  Google Scholar 

  34. 34.

    Nakamae, S. et al. Electronic ground state of heavily overdoped nonsuperconducting La2−xSrxCuO4. Phys. Rev. B 68, 100502R (2003).

    ADS  Article  Google Scholar 

  35. 35.

    Wang, Y. et al. Weak-coupling d-wave BCS superconductivity and unpaired electrons in overdoped La2−xSrxCuO4 single crystals. Phys. Rev. B 76, 064512 (2007).

    ADS  Article  Google Scholar 

  36. 36.

    Michon, B. et al. Thermodynamic evidence of quantum criticality in cuprate superconductors. Preprint at https://arxiv.org/abs/1804.08502 (2018).

  37. 37.

    Davison, R. A., Schalm, K. & Zaanen, J. Holographic duality and the resistivity of strange metals. Phys. Rev. B 89, 245116 (2014).

    ADS  Article  Google Scholar 

  38. 38.

    Hartnoll, S. A. Theory of universal incoherent metallic transport. Nat. Phys. 11, 54–61 (2015).

    Article  Google Scholar 

  39. 39.

    Song, X. Y. et al. Strongly correlated metal built from Sachdev-Ye-Kitaev models. Phys. Rev. Lett. 119, 216601 (2017).

    ADS  Article  Google Scholar 

  40. 40.

    Konstantinovic, Z., Li, Z. Z. & Raffy, H. Temperature dependence of the Hall effect in single-layer and bilayer Bi2Sr2Can–1CunOy thin films at various oxygen contents. Phys. Rev. B 62, R11989(R) (2000).

    ADS  Article  Google Scholar 

  41. 41.

    Charpentier, S. et al. Antiferromagnetic fluctuations and the Hall effect of electron-doped cuprates: possibility of a quantum phase transition at underdoping. Phys. Rev. B 81, 104519 (2010).

    ADS  Article  Google Scholar 

  42. 42.

    Hussey, N. E. et al. Dichotomy in the T-linear resistivity in hole-doped cuprates. Phil. Trans. R. Soc. A 369, 1626–1639 (2011).

    ADS  Article  Google Scholar 

  43. 43.

    Falicov, L. M. & Stachowiak, H. Theory of the de Haas–van Alphen effect in a system of coupled orbits. Application to magnesium. Phys. Rev. 147, 505 (1966).

    ADS  Article  Google Scholar 

Download references


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




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.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

10 Figures, 4 Tables, 11 References

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

Further reading