Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ

Abstract

Close to optimal doping, the copper oxide superconductors show ‘strange metal’ behaviour1,2, suggestive of strong fluctuations associated with a quantum critical point3,4,5,6. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting ‘dome’. The underdoped region of the temperature–doping phase diagram from which superconductivity emerges is referred to as the ‘pseudogap’7,8,9,10,11,12,13 because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: The temperature evolution of resonances in underdoped and overdoped YBCO crystals: superconductivity.
Figure 2: The temperature evolution of resonances across the pseudogap phase boundary.
Figure 3: The phase diagram of YBa2Cu3O6+δ.
Figure 4: The pseudogap boundary inside the superconducting dome.

References

  1. 1

    Ando, Y., Komiya, S., Segawa, K., Ono, S. & Kurita, Y. Electronic phase diagram of high-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature. Phys. Rev. Lett. 93, 267001 (2004)

    ADS  Article  Google Scholar 

  2. 2

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

    ADS  Article  Google Scholar 

  3. 3

    van der Marel, D. et al. Quantum critical behaviour in a high-Tc superconductor. Nature 425, 271–274 (2003)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Orenstein, J. & Millis, A. J. Advances in the physics of high-temperature superconductivity. Nature 288, 468–474 (2000)

    CAS  Google Scholar 

  5. 5

    Varma, C. M., Littlewood, P. B., Schmitt-Rink, S., Abrahams, E. & Ruckenstein, A. Phenomenology of the normal state of Cu–O high-temperature superconductors. Phys. Rev. Lett. 63, 1996–1999 (1989)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Varma, C. M., Nussinov, Z. & van Saarloos, W. Singular or non-Fermi liquids. Phys. Rep. 361, 267417 (2002)

    MathSciNet  Article  Google Scholar 

  7. 7

    Timusk, T. & Statt, B. The pseudogap in high-temperature superconductors: an experimental survey. Rep. Prog. Phys. 62, 61–122 (1999)

    ADS  CAS  Article  Google Scholar 

  8. 8

    Fauqué, B. et al. Magnetic order in the pseudogap phase of high-Tc superconductors. Phys. Rev. Lett. 96, 197001 (2006)

    ADS  Article  Google Scholar 

  9. 9

    Mook, H. A., Sidis, Y., Fauqué, B., Baldent, V. & Bourges, P. Observation of magnetic order in a superconducting YBa2Cu3O6. 6 single crystal using polarized neutron scattering. Phys. Rev. B 78, 020506 (2008)

    ADS  Article  Google Scholar 

  10. 10

    Kaminski, A. et al. Spontaneous breaking of time-reversal symmetry in the pseudogap state of a high-Tc superconductor. Nature 416, 610–613 (2002)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Varma, C. M. Non-Fermi-liquid states and pairing instability of a general model of copper oxide metals. Phys. Rev. B 55, 14554–14580 (1997)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Aji, V. & Varma, C. M. Quantum criticality in dissipative quantum two-dimensional XY and Ashkin–Teller models: application to the cuprates. Phys. Rev. B 79, 184501 (2009)

    ADS  Article  Google Scholar 

  13. 13

    Li, Y. et al. Unusual magnetic order in the pseudogap region of the superconductor HgBa2CuO4+δ . Nature 455, 372–375 (2008)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Migliori, A. & Sarrao, J. M. Resonant Ultrasound Spectroscopy (Wiley-Interscience, 1997)

    Google Scholar 

  15. 15

    Migliori, A. & Maynard, J. D. Implementation of a modern resonant ultrasound spectroscopy system for the measurement of the elastic moduli of small solid specimens. Rev. Sci. Instrum. 76, 121301–121308 (2005)

    ADS  Article  Google Scholar 

  16. 16

    Birss, R. R. Symmetry and Magnetism (Wiley-Interscience Inc., 1964)

    Google Scholar 

  17. 17

    Lei, M. et al. Elastic constants of a monocrystal of superconducting YBa2Cu3O7−δ . Phys. Rev. B 47, 6154–6156 (1993)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Doiron-Leyraud, N. et al. Quantum oscillations and the Fermi surface in an underdoped high-T c superconductor. Nature 447, 565–568 (2007)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Bishop, D. J. et al. Bulk-modulus anomalies at the superconducting transition of single-phase YBa2Cu3O7 . Phys. Rev. B 36, 2408–2410 (1987)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Walstedt, R. E. et al. 63Cu NMR shift and linewidth anomalies in the Tc = 60 K phase of YBaCuO. Phys. Rev. B 41, 9574–9577 (1990)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Vishik, I. M. et al. ARPES studies of cuprate Fermiology: superconductivity, pseudogap and quasiparticle dynamics. New J. Phys. 12, 105008 (2010)

    ADS  Article  Google Scholar 

  22. 22

    Daou, R. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Kondo, T. et al. Disentangling Cooper-pair formation above the transition temperature from the pseudogap state in the cuprates. Nature Phys. 7, 21–25 (2011)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Leridon, B., Monod, P. & Colson, D. Thermodynamic signature of a phase transition in the pseudogap phase of YBa2Cu3Ox high-Tc superconductor. Europhys. Lett. 87, 17011 (2009)

    ADS  Article  Google Scholar 

  25. 25

    Bhatia, A. B. Ultrasonic Absorption (Clarendon Press, 1967)

    Google Scholar 

  26. 26

    Landau, L. D. & Khalatnikov, I. M. On the anomalous absorption of a sound near to points of phase transition of the second kind. Dokl. Akad. Nauk SSSR 96, 469–472 (1954)

    Google Scholar 

  27. 27

    Xia, J. et al. Polar Kerr-effect measurements of the high-temperature YBa2Cu3O6+x superconductor: evidence for broken symmetry near the pseudogap temperature. Phys. Rev. Lett. 100, 127002 (2008)

    ADS  Article  Google Scholar 

  28. 28

    Chang, J. et al. Direct observation of competition between superconductivity and charge density wave order in YBa2Cu3O6. 67 . Nature Phys. 8, 871–876 (2012)

    ADS  CAS  Article  Google Scholar 

  29. 29

    Varshni, Y. Temperature dependence of the elastic constants. Phys. Rev. B 2, 3952–3958 (1970)

    ADS  Article  Google Scholar 

  30. 30

    Liang, R., Hardy, W. N. & Bonn, D. A. Evaluation of CuO2 plane hole doping in YBa2Cu3O6+x single crystals. Phys. Rev. B 73, 180505 (2006)

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank E. Abrahams, J. Analytis, P. Bourges, A. Finkel’stein, M. Greven, N. Harrison, K. Modic, C. Varma, I. Vishik and G. Yu for critical reading of the manuscript and informative discussions. Work at Los Alamos National Laboratory (LANL) was supported by National Science Foundation grant DMR-0654118, by the US Department of Energy and by the State of Florida. LANL is operated by LANS LLC. Work at the University of British Columbia was supported by the Canadian Institute for Advanced Research and the Natural Science and Engineering Research Council.

Author information

Affiliations

Authors

Contributions

A.S., J.B.B., S.C.R., R.D.McD. and A.M. designed the experiment. A.S., J.B.B. and A.M. built the electronic circuits and the RUS probe. A.S. and F.F.B. wrote the software and analysed the results. B.J.R., R.L., W.N.H. and D.A.B. prepared the YBCO crystals. A.S., B.J.R., R.D.McD. and A.M. wrote the manuscript.

Corresponding author

Correspondence to Arkady Shekhter.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data 1-2, additional references and Supplementary Figures 1-2. (PDF 1299 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shekhter, A., Ramshaw, B., Liang, R. et al. Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ. Nature 498, 75–77 (2013). https://doi.org/10.1038/nature12165

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing