In underdoped cuprate superconductors, phase stiffness is low and long-range superconducting order is destroyed readily by thermally generated vortices (and anti-vortices), giving rise to a broad temperature regime above the zero-resistive state in which the superconducting phase is incoherent1,2,3,4. It has often been suggested that these vortex-like excitations are related to the normal-state pseudogap or some interaction between the pseudogap state and the superconducting state5,6,7,8,9,10. However, to elucidate the precise relationship between the pseudogap and superconductivity, it is important to establish whether this broad phase-fluctuation regime vanishes, along with the pseudogap11, in the slightly overdoped region of the phase diagram where the superfluid pair density and correlation energy are both maximal12. Here we show, by tracking the restoration of the normal-state magnetoresistance in overdoped La2−xSrxCuO4, that the phase-fluctuation regime remains broad across the entire superconducting composition range. The universal low phase stiffness is shown to be correlated with a low superfluid density1, a characteristic of both underdoped and overdoped cuprates12,13,14. The formation of the pseudogap, by inference, is therefore both independent of and distinct from superconductivity.

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  1. 1.

    & Importance of phase fluctuations in superconductors with small superfluid density. Nature 374, 434–437 (1995).

  2. 2.

    , , , & Vanishing of phase coherence in underdoped Bi2Sr2CaCu2O8+δ. Nature 398, 221–223 (1999).

  3. 3.

    , , , & Vortex-like excitations and the onset of superconducting phase fluctuation in underdoped La2−xSrxCuO4. Nature 406, 486–488 (2000).

  4. 4.

    et al. Field-enhanced diamagnetism in the pseudogap state of the cuprate Bi2Sr2CaCu2O8+δ superconductor in an intense magnetic field. Phys. Rev. Lett. 95, 247002 (2005).

  5. 5.

    et al. Spectroscopic evidence for a pseudogap in the normal state of underdoped high-Tc superconductors. Nature 382, 51–54 (1996).

  6. 6.

    et al. Temperature and doping dependence of the Bi–Sr–Ca–Cu–O electronic structure and fluctuation effects. Phys. Rev. B 56, 14185–14189 (1997).

  7. 7.

    & Ginzburg–Landau theory of the spin-charge-separated system. Phys. Rev. B 45, 966–970 (1992).

  8. 8.

    , , & Pairing and spin gap in the normal state of short coherence length superconductors. Phys. Rev. Lett. 69, 2001–2004 (1992).

  9. 9.

    et al. Two-gap model for underdoped cuprate superconductors. Phys. Rev. B 62, R9295–R9298 (2000).

  10. 10.

    et al. Spectroscopic fingerprint of phase-incoherent superconductivity in the underdoped Bi2Sr2CaCu2O8+δ. Science 325, 1099–1103 (2009).

  11. 11.

    & The doping dependence of T*—what is the real high-Tc phase diagram? Physica 349C, 53–68 (2001).

  12. 12.

    et al. Anomalous peak in the superconducting condensate density of cuprate high-Tc superconductors at a unique doping state. Phys. Rev. Lett. 86, 1614–1617 (2001).

  13. 13.

    et al. Magnetic-field penetration depth in Tl2Ba2CuO6+δ in the overdoped regime. Nature 364, 605–607 (1993).

  14. 14.

    et al. Muon spin rotation study of the correlation between Tc and ns/m* in overdoped Tl2Ba2CuO6+δ. Phys. Rev. Lett. 71, 1764–1767 (1993).

  15. 15.

    et al. Resistive upper critical fields and irreversibility lines of optimally doped high-Tc cuprates. Phys. Rev. B 60, 12475–12479 (1999).

  16. 16.

    et al. Total suppression of superconductivity by high magnetic fields in YBa2Cu3O6.6. Phys. Rev. Lett. 99, 027003 (2007).

  17. 17.

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

  18. 18.

    Magnetoresistance in Metals (Cambridge Univ. Press, 1989).

  19. 19.

    et al. In-plane and out-of-plane magnetoresistance in La2−xSrxCuO4 single crystals. Phys. Rev. B 53, 8733–8742 (1996).

  20. 20.

    et al. Electron pockets in the Fermi surface of hole-doped high-Tc superconductors. Nature 450, 533–536 (2007).

  21. 21.

    et al. Fermi-surface reconstruction and two-carrier model for the Hall effect in YBa2Cu4O8. Phys. Rev. B 82, 020514(R) (2010).

  22. 22.

    et al. High field phase diagram of cuprates derived from the Nernst effect. Phys. Rev. Lett. 88, 257003 (2002).

  23. 23.

    & Topological excitations in two-dimensional superconductors. Phys. Rev. Lett. 42, 1169–1172 (1979).

  24. 24.

    , & Nernst effect in high-Tc superconductors. Phys. Rev. B 73, 024510 (2006).

  25. 25.

    & Doping dependence of the upper critical field in La2−xSrxCuO4 from specific heat. Europhys. Lett. 81, 57007 (2008).

  26. 26.

    et al. Dichotomy in the T-linear resistivity in high-Tc cuprates. Preprint at .

  27. 27.

    et al. Crossover from coherent to incoherent electronic excitations in the normal state of Bi2Sr2CaCu2O8+δ. Phys. Rev. Lett. 90, 207003 (2003).

  28. 28.

    et al. Universal correlations between Tc and ns/m* (carrier density over effective mass) in high-Tc cuprate superconductors. Phys. Rev. Lett. 62, 2317–2320 (1989).

  29. 29.

    et al. Nernst effect and disorder in the normal state of high-Tc cuprates. Phys. Rev. Lett. 96, 067002 (2006).

  30. 30.

    , , , & Electronic phase diagram of high-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature. Phys. Rev. Lett. 93, 267001 (2004).

  31. 31.

    et al. Generic superconducting phase behaviour in high-Tc cuprates: Tc variation with hole concentration in YBa2Cu3O7−δ. Phys. Rev. B 51, 12911–12914 (1995).

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The authors would like to acknowledge R. A. Cooper for experimental assistance, S. M. Hayden and O. J. Lipscombe for providing us with the LSCO23 crystals, and J. P. Annett, A. Carrington, B. Gyorffy, R. H. McKenzie, T. Senthil, N. Shannon, T. Timusk, Y. J. Uemura and J. A. Wilson for fruitful discussions. This work was supported by EPSRC (UK), MEXT-CT-2006-039047, EURYI, the National Research Foundation, Singapore and EuroMagNET under EU contract 228043. N.E.H. acknowledges a Royal Society Wolfson Research Merit Award.

Author information


  1. H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol, BS8 1TL, UK

    • Patrick M. C. Rourke
    • , Ioanna Mouzopoulou
    •  & Nigel E. Hussey
  2. Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 637371 Singapore, Singapore

    • Xiaofeng Xu
    •  & Christos Panagopoulos
  3. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China

    • Xiaofeng Xu
  4. Department of Physics, University of Crete and FORTH, 71003 Heraklion, Greece

    • Christos Panagopoulos
  5. State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Beijing 100871, China

    • Yue Wang
  6. Laboratoire National des Champs Magnetiques Intenses (CNRS, INSA, UJF, UPS), Toulouse 31400, France

    • Baptiste Vignolle
    •  & Cyril Proust
  7. High Field Magnet Laboratory, Institute for Molecules and Materials, Radboud University Nijmegen, Toernooiveld 7, 6525 ED Nijmegen, The Netherlands

    • Evgenia V. Kurganova
    •  & Uli Zeitler
  8. Department of Applied Physics, Graduate School of Engineering, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan

    • Yoichi Tanabe
    • , Tadashi Adachi
    •  & Yoji Koike


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All authors made critical comments on the manuscript. Y.T., T.A. and Y.K. synthesized the samples. P.M.C.R., I.M., X.X., Y.W., B.V., C.P., E.V.K., U.Z. and N.E.H. carried out the transport measurements. P.M.C.R., I.M. and N.E.H. analysed and interpreted the transport data.

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The authors declare no competing financial interests.

Corresponding author

Correspondence to Nigel E. Hussey.

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