Ultrasound evidence for a two-component superconducting order parameter in Sr2RuO4

A Publisher Correction to this article was published on 28 October 2020

This article has been updated


The quasi-two-dimensional metal Sr2RuO4 is one of the best characterized unconventional superconductors, yet the nature of its superconducting order parameter is still under debate1,2,3. This information is crucial to determine the pairing mechanism of Cooper pairs. Here we use ultrasound velocity to probe the superconducting state of Sr2RuO4. This thermodynamic probe is sensitive to the symmetry of the material, and therefore, it can help in identifying the symmetry of the superconducting order parameter4,5. Indeed, we observe a sharp jump in the shear elastic constant c66 as the temperature is increased across the superconducting transition. This directly implies that the superconducting order parameter is of a two-component nature. On the basis of symmetry arguments and given the other known properties of Sr2RuO4 (refs. 6,7,8), we discuss which states are compatible with this requirement and propose that the two-component order parameter {dxz; dyz} is the most likely candidate.

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Fig. 1: Relative change in the sound velocity of Sr2RuO4 through Tc.
Fig. 2: Jump in the c66 shear modulus at Tc.

Data availability

All data that support the findings of this study are available from the corresponding authors on request.

Change history

  • 28 October 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.


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We thank J. Chang, J.C. Davis, C. Kallin, S.A. Kivelson, D. LeBoeuf, W.A. MacFarlane, A.P. Mackenzie, V. Madhavan, B.J. Ramshaw, G. Rikken, M. Sigrist, D. Vignolles and M.B. Walker for helpful and stimulating discussions. Part of this work, associated with the PhD thesis of C.L. working with C.P. under the supervision of L.T., was performed at the University of Toronto. C.P. acknowledges support from the EUR grant NanoX no. ANR-17-EURE-0009 and from the ANR grant NEPTUN no. ANR-19-CE30-0019-01. L.T. acknowledges support from the Canadian Institute for Advanced Research (CIFAR) as a CIFAR Fellow and funding from the Natural Sciences and Engineering Research Council of Canada (NSERC; PIN: 123817), the Fonds de recherche du Québec—Nature et Technologies (FRQNT), the Canada Foundation for Innovation (CFI) and a Canada Research Chair. This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund. Y.M. acknowledges support from JSPS Kakenhi (grants JP15H5852, JP15K21717 and JP17H06136) and the JSPS-EPSRC Core-to-Core Program of Oxide Superspin (OSS). A.G. acknowledges the support of the European Research Council (ERC-319286-QMAC). The Flatiron Institute is a division of the Simons Foundation.

Author information




C.L. and C.P. performed the ultrasound measurements in Toronto. S.B., L.B. and C.P. performed the ultrasound measurements in Toulouse. S.B., C.L., L.B., M.D. and C.P. analysed the data. I.P. performed the calculations, with input from A.G. M.N. and A.Z. conceived and realized the 3He cryostat in Toulouse. Z.Q.M. and Y.M. prepared and characterized the Sr2RuO4 sample. I.P., L.T. and C.P. wrote the manuscript in consultation with all the authors. I.P., L.T. and C.P. co-supervised the project.

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Correspondence to I. Paul or L. Taillefer or C. Proust.

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Supplementary Information

Supplementary Figs. 1 and 2, discussion and Table 1.

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Benhabib, S., Lupien, C., Paul, I. et al. Ultrasound evidence for a two-component superconducting order parameter in Sr2RuO4. Nat. Phys. (2020). https://doi.org/10.1038/s41567-020-1033-3

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