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Angle-resolved phase-sensitive determination of the in-plane gap symmetry in YBa2Cu3O7−δ

An Erratum to this article was published on 01 May 2006


Understanding the nature of the ground state and its low-lying excitations in the copper oxide superconductors is a prerequisite for determining the origin of high-temperature superconductivity. A superconducting order parameter (that is, the energy gap) with a predominantly d X 2 Y 2 symmetry is well-established. However, various deviations from a pure d-wave pair state, such as the possibility of Cooper pairing with broken time-reversal symmetry or an admixed d X 2 Y 2 +s pair state, have been theoretically predicted and actively sought in numerous experimental studies. Here, we present an angle-resolved phase-sensitive technique for accurately determining the in-plane pairing symmetry, and demonstrate this technique in optimally doped YBa2Cu3O7−δ. We find that the gap along the b-axis (Cu–O chain) direction is at least 20% larger than that along the a-axis direction, and that any imaginary i dx y, is or ip component must be smaller than a few per cent of the d X 2 Y 2 component of the gap.

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Figure 1: Experimental ring geometry.
Figure 2: Schematic and SQUID microscope images of the rings of sample 1.
Figure 3: Integrated flux through the rings of sample 1, as a function of θ, the angle of the second junction normal relative to the majority twin a-axis direction.
Figure 4: SQUID images of sample 2.
Figure 5: Integrated flux through the rings of sample 2, as a function of θ, the second junction normal angle relative to the majority twin a-axis direction.


  1. van Harlingen, D. J. Phase-sensitive tests of the symmetry of the pairing state in the high-temperature superconductors-evidence for d x 2 − y 2 symmetry. Rev. Mod. Phys. 67, 515–535 (1995).

    Article  ADS  Google Scholar 

  2. Tsuei, C. C. & Kirtley, J. R. Pairing symmetry in cuprate superconductors. Rev. Mod. Phys. 72, 969–1016 (2000).

    Article  ADS  Google Scholar 

  3. Tsuei, C. C. & Kirtley, J. R. Phase-sensitive evidence for d-wave pairing symmetry in electron-doped cuprate superconductors. Phys. Rev. Lett. 85, 182–185 (2000).

    Article  ADS  Google Scholar 

  4. Tsuei, C. C. et al. Robust d x 2 − y 2 pairing symmetry in high-temperature superconductors. Phys. Rev. Lett. 93, 187004 (2004).

    Article  ADS  Google Scholar 

  5. Laughlin, R. B. The relationship between high-temperature superconductivity and the fractional quantum hall effect. Science 242, 525–533 (1988).

    Article  ADS  Google Scholar 

  6. Varma, C. M. Pseudogap phase and the quantum-critical point in copper-oxide metals. Phys. Rev. Lett. 83, 3538–3541 (1999).

    Article  ADS  Google Scholar 

  7. Sigrist, M. Time-reversal symmetry breaking states in high-temperature superconductors. Prog. Theor. Phys. 99, 899–929 (1998).

    Article  ADS  Google Scholar 

  8. Löfwander, T., Shumeiko, V. S. & Wendin, G. Andreev bound states in high-Tc superconducting junctions. Supercond. Sci. Technol. 14, R53–R77 (2001).

    Article  ADS  Google Scholar 

  9. Spielman, S. et al. Measurement of the spontaneous polar Kerr effect in YBa2Cu3O7 and Bi2Sr2CaCu2O8 . Phys. Rev. Lett. 68, 3472–3475 (1992).

    Article  ADS  Google Scholar 

  10. Lawrence, T. W., Szöker, A. & Laughlin, R. B. Absence of circular dichroism in high-temperature superconductors. Phys. Rev. Lett. 69, 1439–1442 (1992).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Simon, M. E. & Varma, C. M. Detection and implications of a time-reversal breaking state in underdoped cuprates. Phys. Rev. Lett. 89, 247003 (2002).

    Article  ADS  Google Scholar 

  13. Fauqué, B. et al. Magnetic order in the pseudogap phase of high-Tc superconductors. Preprint at <> 2005.

  14. Covington, M. et al. Observation of surface-induced broken time-reversal symmetry in YBa2Cu3O7 tunnel junctions. Phys. Rev. Lett. 79, 277–280 (1997).

    Article  ADS  Google Scholar 

  15. Dagan, Y. & Deutscher, G. Doping and magnetic field dependence of in-plane tunneling into YBa2Cu3O7−x: possible evidence for the existence of a quantum critical point. Phys. Rev. Lett. 87, 177004 (2001).

    Article  ADS  Google Scholar 

  16. Sharoni, A. et al. Local and macroscopic tunneling spectroscopy of Y1−xCaxBa2Cu3O7−δ films: evidence for a doping-dependentis orid xy component in the order parameter. Phys. Rev. B 65, 134526 (2002).

    Article  ADS  Google Scholar 

  17. Mathai, A., Gim, Y., Black, R. C., Amar, A. & Wellstood, F. C. Experimental proof of a time-reversal-invariant order parameter with a π shift in YBa2Cu3O7−δ . Phys. Rev. Lett. 74, 4523–4526 (1995).

    Article  ADS  Google Scholar 

  18. Schulz, R. R. et al. Design and realization of an all d-wave dc π-superconducting quantum interference device. Appl. Phys. Lett. 76, 912–914 (2002).

    Article  ADS  Google Scholar 

  19. Beasley, M. R., Lew, D. & Laughlin, R. B. Time-reversal symmetry breaking in superconductors: a proposed experimental test. Phys. Rev. B 49, 12330–12332 (1994).

    Article  ADS  Google Scholar 

  20. Ng, T.-K. & Varma, C. M. Experimental signatures of time-reversal-violating superconductors. Phys. Rev. B 70, 054514 (2004).

    Article  ADS  Google Scholar 

  21. Polturak, E., Koren, G., Cohen, D. & Aharoni, E. Measurements of the anisotropy and temperature dependence of the in-plane energy gap in YBa2Cu3O7−δ using Andreev reflections. Phys. Rev. B 47, 5270–5274 (1993).

    Article  ADS  Google Scholar 

  22. Basov, D. N. et al. In-plane anisotropy of the penetration depth in YBa2Cu3O7−x and YBa2Cu4O8 superconductors. Phys. Rev. Lett. 74, 598–601 (1995).

    Article  ADS  Google Scholar 

  23. Limonov, M. F., Rykov, A. I. & Tajima, S. Raman scattering study on fully oxygenated YBa2Cu3O7 single crystals:xy anisotropy in the superconductivity-induced effects. Phys. Rev. Lett. 80, 825–828 (1998).

    Article  ADS  Google Scholar 

  24. Lu, D. H. et al. Superconducting gap and strong in-plane anisotropy in untwinned YBa2Cu3O7−δ . Phys. Rev. Lett. 86, 4370–4373 (2001).

    Article  ADS  Google Scholar 

  25. Engelhardt, A., Dittmann, R. & Braginski, A. I. Subgap conductance features of YBa2Cu3O7−δ edge Josephson junctions. Phys. Rev. B 59, 3815–3822 (1999).

    Article  ADS  Google Scholar 

  26. Smilde, H. J. H. et al. Admixtures to d-wave gap symmetry in untwinned YBa2Cu3O7 superconducting films measured by angle-resolved electron tunneling. Phys. Rev. Lett. 95, 257001 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Gim, Y., Mathai, A., Black, R., Amar, A. & Wellstood, F. C. Angular dependence of the symmetry of the order parameter in YBa2Cu3O7−δ . IEEE Trans. Appl. Supercond. 7, 2331–2334 (1997).

    Article  ADS  Google Scholar 

  29. van Harlingen, D. J., Hilliard, J. E., Plourde, B. L. T. & Yanoff, B. D. Extending SQUID interferometry beyond the cuprates and beyond d-wave symmetry. Physica C 317–318, 410–420 (1999).

    Article  ADS  Google Scholar 

  30. Clem, J. R. American Physical Society, Annual March Meeting, 1998, Abstract K36.06 (American Physical Society, College Park, Maryland, 1998).

    Google Scholar 

  31. Smilde, H. J. H., Hilgenkamp, H., Rijnders, G., Rogalla, H. & Blank, D. H. A. Enhanced transparency ramp-type Josephson contacts through interlayer deposition. Appl. Phys. Lett. 80, 4579–4581 (2002).

    Article  ADS  Google Scholar 

  32. Dekkers, J. M. et al. Monocrystalline YBa2Cu3O7−x thin films on vicinal SrTiO3 (001) substrates. Appl. Phys. Lett. 83, 5199–5201 (2003).

    Article  ADS  Google Scholar 

  33. Kirtley, J. R. et al. High-resolution integrated scanning SQUID microscope. Appl. Phys. Lett. 66, 1138–1140 (1995).

    Article  ADS  Google Scholar 

  34. Sigrist, M. & Rice, T. M. Paramagnetic effect in high-T c superconductors-a hint for d-wave superconductivity. J. Phys. Soc. Jpn 61, 4283–4286 (1992).

    Article  ADS  Google Scholar 

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We would like to thank D. Blank, A. Brinkman, M. Dekkers, A. Golubov, R. Koch, D. Newns, G. Rijnders, F. Roesthuis, H. Rogalla, H.-J. Smilde and C. Varma for discussions. This work was supported by the Dutch Foundation for Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO), the Dutch STW NanoNed programme, the European Science Foundation (ESF) PiShift programme, and by the Center for Probing the Nanoscale (CPN), an NSF NSEC, NSF Grant No. PHY-0425897.

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Kirtley, J., Tsuei, C., Ariando et al. Angle-resolved phase-sensitive determination of the in-plane gap symmetry in YBa2Cu3O7−δ. Nature Phys 2, 190–194 (2006).

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