Letter | Published:

Dependence of the critical temperature in overdoped copper oxides on superfluid density

Nature volume 536, pages 309311 (18 August 2016) | Download Citation

Abstract

The physics of underdoped copper oxide superconductors, including the pseudogap, spin and charge ordering and their relation to superconductivity1,2,3, is intensely debated. The overdoped copper oxides are perceived as simpler, with strongly correlated fermion physics evolving smoothly into the conventional Bardeen–Cooper–Schrieffer behaviour. Pioneering studies on a few overdoped samples4,5,6,7,8,9,10,11 indicated that the superfluid density was much lower than expected, but this was attributed to pair-breaking, disorder and phase separation. Here we report the way in which the magnetic penetration depth and the phase stiffness depend on temperature and doping by investigating the entire overdoped side of the La2−xSrxCuO4 phase diagram. We measured the absolute values of the magnetic penetration depth and the phase stiffness to an accuracy of one per cent in thousands of samples; the large statistics reveal clear trends and intrinsic properties. The films are homogeneous; variations in the critical superconducting temperature within a film are very small (less than one kelvin). At every level of doping the phase stiffness decreases linearly with temperature. The dependence of the zero-temperature phase stiffness on the critical superconducting temperature is generally linear, but with an offset; however, close to the origin this dependence becomes parabolic. This scaling law is incompatible with the standard Bardeen–Cooper–Schrieffer description.

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Acknowledgements

A. Gozar, J. Zhang and J. Yoon contributed to developing the characterization techniques during the early stages of this work. R. Sundling developed the software for the inversion of the inductance data. We also benefited from the electrolyte-gating experiments and X-ray diffraction studies by X. Leng, and from numerical simulations by N. Božović. The research was done at BNL and was supported by the US Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division. X.H. is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4410. I.B. acknowledges discussions with J. Zaanen, G. Deutscher, A. Leggett, P. Littlewood, C.-B. Eom, J. Mannhart, P. Coleman, R. Prozorov, D. van der Marel, A. McKenzie, V. Kogan, P. Armitage, J.-M. Triscone, P. Canfield, A. Chubukov, B. Halperin, P. Kim, T. Lemberger, M. V. Sadovskii, D. Pavuna, Z. Radović and M. Vanević.

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Affiliations

  1. Brookhaven National Laboratory, Upton, New York 11973-5000, USA

    • I. Božović
    • , X. He
    • , J. Wu
    •  & A. T. Bollinger
  2. Applied Physics Department, Yale University, New Haven, Connecticut 06520, USA

    • I. Božović
    •  & X. He

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Contributions

I.B. conceived the project, synthesized the films using ALL-MBE, measured the inductance, analysed the data and wrote the text. X.H. synthesized the films, performed AFM imaging and measured the inductance. A.T.B. fabricated the devices by lithography and performed the inductance measurements in the 3He system. J.W. performed the transport measurements.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to I. Božović.

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https://doi.org/10.1038/nature19061

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