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.

This is a preview of subscription content

## Access options

\$32.00

All prices are NET prices.

## References

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)

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

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

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

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)

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

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

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

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)

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)

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)

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)

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

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

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)

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

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

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

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

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)

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

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

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)

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)

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

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)

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)

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)

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

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)

## 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

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.

## 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)

## Rights and permissions

Reprints and Permissions

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

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/nature12165

• ### Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

• Shuqiu Wang
• Peayush Choubey
• J. C. Séamus Davis

Nature Communications (2021)

• ### Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa2Cu4O8

• Wen Wang
• Jun Luo
• Guo-Qing Zheng

Science China Physics, Mechanics & Astronomy (2021)

• ### Field-dependent specific heat of the canonical underdoped cuprate superconductor $$\hbox {YBa}_2\hbox {Cu}_4\hbox {O}_8$$

• Jeffery L. Tallon
• John W. Loram

Scientific Reports (2020)

• ### Quantized Repetitions of the Cuprate Pseudogap Line

• Vincent Sacksteder

Journal of Superconductivity and Novel Magnetism (2020)

• ### Evolution of Pairing Orders between Pseudogap and Superconducting Phases of Cuprate Superconductors

• Wei-Lin Tu
• Ting-Kuo Lee

Scientific Reports (2019)