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# Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor

## Abstract

The nature of the pseudogap phase is a central problem in the effort to understand the high-transition-temperature (high-Tc) copper oxide superconductors1. A fundamental question is what symmetries are broken when the pseudogap phase sets in, which occurs when the temperature decreases below a value T*. There is evidence from measurements of both polarized neutron diffraction2,3 and the polar Kerr effect4 that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements5 and inelastic neutron scattering6,7,8 at low doping, and from scanning tunnelling spectroscopy9,10 at low temperature, but showed no clear relation to T*. Here we report the observation of a large in-plane anisotropy of the Nernst effect in YBa2Cu3O y that sets in precisely at T* throughout the doping phase diagram. We show that the CuO chains of the orthorhombic lattice are not responsible for this anisotropy, which is therefore an intrinsic property of the CuO2 planes. We conclude that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order11,12.

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## References

1. Norman, M. R., Pines, D. & Kallin, C. The pseudogap: friend or foe of high T c? Adv. Phys. 54, 715–733 (2005)

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

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

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

5. Ando, Y. et al. Electrical resistivity anisotropy from self-organized one dimensionality in high-temperature superconductors. Phys. Rev. Lett. 88, 137005 (2002)

6. Stock, C. et al. Dynamical stripes and resonance in the superconducting and normal phases of YBa2Cu3O6. 5 ortho-II superconductor. Phys. Rev. B 69, 014502 (2004)

7. Hinkov, V. et al. Spin dynamics in the pseudogap state of a high-temperature superconductor. Nature Phys. 3, 780–785 (2007)

8. Hinkov, V. et al. Electronic liquid crystal state in the high-temperature superconductor YBa2Cu3O6. 45 . Science 319, 597–600 (2008)

9. Kohsaka, Y. et al. An intrinsic bond-centered electronic glass with unidirectional domains in underdoped cuprates. Science 315, 1380–1385 (2007)

10. Kohsaka, Y. et al. How Cooper pairs vanish approaching the Mott insulator in Bi2Sr2CaCu2O8+δ . Nature 454, 1072–1078 (2008)

11. Kivelson, S. A. et al. How to detect fluctuating stripes in the high-temperature superconductors. Rev. Mod. Phys. 75, 1201–1241 (2003)

12. Vojta, M. Lattice-symmetry breaking in cuprate superconductors: stripes, nematics and superconductivity. Adv. Phys. 58, 699–820 (2009)

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

14. Wang, Y., Li, P. & Ong, N. P. Nernst effect in high-T c superconductors. Phys. Rev. B 73, 024510 (2006)

15. Rullier-Albenque, F. et al. Nernst effect and disorder in the normal state of high-T c cuprates. Phys. Rev. Lett. 96, 067002 (2006)

16. Ong, N. P. et al. Vorticity and the Nernst effect in cuprate superconductors. Ann. Phys. (Leipz.) 13, 9–14 (2004)

17. Behnia, K. The Nernst effect and the boundaries of the Fermi liquid picture. J. Phys. Condens. Matter 21, 113101 (2009)

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

19. Ando, Y. et al. Electronic phase diagram of high-T c cuprate superconductors from a mapping of the in-plane resistivity curvature. Phys. Rev. Lett. 93, 267001 (2004)

20. Matusiak, M. et al. Influence of the pseudogap on the Nernst coefficient of Y0. 9Ca0. 1Ba2Cu3O y . Europhys. Lett. 86, 17005 (2009)

21. Borzi, R. A. et al. Formation of a nematic fluid at high fields in Sr3Ru2O7 . Science 315, 214–217 (2007)

22. Hackl, A., Vojta, M. & Sachdev, S. Quasiparticle Nernst effect in stripe-ordered cuprates. Preprint at 〈http://arXiv.org/abs/0908.1088〉 (2009)

23. Hackl, A. & Vojta, M. Nernst effect anisotropy as a sensitive probe of Fermi surface distortions from electron-nematic order. Preprint at 〈http://arXiv.org/abs/0909.4534v2〉 (2009)

24. Cyr-Choinière, O. et al. Enhancement of the Nernst effect by stripe order in a high-T c superconductor. Nature 458, 743–745 (2009)

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

26. Ichikawa, N. et al. Local magnetic order vs superconductivity in a layered cuprate. Phys. Rev. Lett. 85, 1738–1741 (2000)

27. Taillefer, L. Fermi surface reconstruction in high-T c superconductors. J. Phys. Condens. Matter 21, 164212 (2009)

28. Chang, J. et al. Thermo-electric study of Fermi surface reconstruction in YBa2Cu3O y . Preprint at 〈http://arXiv.org/abs/0907.5039〉 (2009)

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

30. Kivelson, S. A., Fradkin, E. & Emery, V. J. Electronic liquid-crystal phases of a doped Mott insulator. Nature 393, 550–553 (1998)

## Acknowledgements

We thank K. Behnia, R. L. Greene, C. Kallin, S. A. Kivelson, A. J. Millis, C. Proust, S. Sachdev, A.-M. S. Tremblay and M. Vojta for discussions, and J. Corbin for his assistance with the experiments. J.C. was supported by fellowships from the Swiss National Science Foundation and the Fonds québécois de la recherche sur la nature et les technologies (FQRNT). L.T. acknowledges support from the Canadian Institute for Advanced Research and funding from the Canadian Natural Sciences and Engineering Research Council, the FQRNT, the Canada Foundation for Innovation and a Canada Research Chair.

Author Contributions R.D., J.C., D.L., O.C.-C., F.L. and N.D.-L. performed the Nernst and resistivity measurements; R.D., J.C. and D.L. analysed the Nernst data; B.J.R., R.L., D.A.B. and W.N.H. prepared the samples at the University of British Columbia (crystal growth, annealing, de-twinning, contacts); and L.T. supervised the project and wrote the manuscript.

## Author information

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Correspondence to Louis Taillefer.

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### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary Information

This file contains a Supplementary Discussion, Supplementary Data, Supplementary Table S1, Supplementary Figure S1-S9 with Legends and Supplementary References. (PDF 1558 kb)

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Daou, R., Chang, J., LeBoeuf, D. et al. Broken rotational symmetry in the pseudogap phase of a high-Tc superconductor. Nature 463, 519–522 (2010). https://doi.org/10.1038/nature08716

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• DOI: https://doi.org/10.1038/nature08716

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