- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Impurity-induced double transitions for accidentally degenerate unconventional pairing states

Bastian Zinkl and Manfred Sigrist

  • Institute for Theoretical Physics, ETH Zurich, 8093 Zurich, Switzerland

PDF

Phys. Rev. Research 3, L012004 – Published 14 January, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L012004

Abstract

Nonmagnetic impurities can lift the accidental degeneracy of unconventional pairing states, such as the (d+ig)-wave state recently proposed for Sr2RuO4. This type of effect would lead to a superconducting double transition upon impurity doping. In a model calculation it is shown how this behavior depends on material parameters and how it could be detected.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (27)

  1. G. M. Luke, Y. Fudamoto, K. Kojima, M. Larkin, J. Merrin, B. Nachumi, Y. Uemura, Y. Maeno, Z. Mao, Y. Mori et al., Time-reversal symmetry-breaking superconductivity in Sr2RuO4, Nature (London) 394, 558 (1998).
  2. A. P. Mackenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing, Rev. Mod. Phys. 75, 657 (2003).
  3. J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and A. Kapitulnik, High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time-Reversal Symmetry in the Superconducting State, Phys. Rev. Lett. 97, 167002 (2006).
  4. Y. Maeno, S. Kittaka, T. Nomura, S. Yonezawa, and K. Ishida, Evaluation of spin-triplet superconductivity in Sr2RuO4, J. Phys. Soc. Jpn. 81, 011009 (2011).
  5. A. Pustogow, Y. Luo, A. Chronister, Y.-S. Su, D. Sokolov, F. Jerzembeck, A. P. Mackenzie, C. Hicks, N. Kikugawa, S. Raghu et al., Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance, Nature (London) 574, 72 (2019).
  6. K. Ishida, M. Manago, K. Kinjo, and Y. Maeno, Reduction of the O17 knight shift in the superconducting state and the heat-up effect by NMR pulses on Sr2RuO4, J. Phys. Soc. Jpn. 89, 034712 (2020).
  7. A. Chronister, A. Pustogow, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, C. W. Hicks, A. P. Mackenzie, E. D. Bauer, and S. E. Brown, Evidence for even parity unconventional superconductivity in Sr2RuO4, arXiv:2007.13730.
  8. E. Hassinger, P. Bourgeois-Hope, H. Taniguchi, S. Rene de Cotret, G. Grissonnanche, M. S. Anwar, Y. Maeno, N. Doiron-Leyraud, and L. Taillefer, Vertical Line Nodes in the Superconducting Gap Structure of Sr2RuO4, Phys. Rev. X 7, 011032 (2017).
  9. R. Sharma, S. D. Edkins, Z. Wang, A. Kostin, C. Sow, Y. Maeno, A. P. Mackenzie, J. C. S. Davis, and V. Madhavan, Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging, Proc. Natl. Acad. Sci. U. S. A. 117, 5222 (2020).
  10. Y. S. Li, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, A. S. Gibbs, Y. Maeno, C. W. Hicks, M. Nicklas, and A. P. Mackenzie, High sensitivity heat capacity measurements on Sr2RuO4 under uniaxial pressure, arXiv:1906.07597.
  11. V. Grinenko, S. Ghosh, R. Sarkar, J.-C. Orain, A. Nikitin, M. Elender, D. Das, Z. Guguchia, F. Brückner, M. E. Barber et al., Split superconducting and time-reversal symmetry-breaking transitions, and magnetic order in Sr2RuO4 under uniaxial stress, arXiv:2001.08152.
  12. S. A. Kivelson, A. C. Yuan, B. Ramshaw, and R. Thomale, A proposal for reconciling diverse experiments on the superconducting state in Sr2RuO4, npj Quantum Mater. 5, 43 (2020).
  13. S. Ghosh, A. Shekhter, F. Jerzembeck, N. Kikugawa, D. A. Sokolov, M. Brando, A. P. Mackenzie, C. W. Hicks, and B. J. Ramshaw, Thermodynamic evidence for a two-component superconducting order parameter in Sr2RuO4, Nat. Phys. (2020), doi:10.1038/s41567-020-1032-4.
  14. R. Willa, Symmetry-mixed bound-state order, Phys. Rev. B 102, 180503(R) (2020).
  15. A. T. Rømer, D. D. Scherer, I. M. Eremin, P. J. Hirschfeld, and B. M. Andersen, Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr2RuO4, Phys. Rev. Lett. 123, 247001 (2019).
  16. I. Žutić and I. Mazin, Phase-Sensitive Tests of the Pairing State Symmetry in Sr2RuO4, Phys. Rev. Lett. 95, 217004 (2005).
  17. H. G. Suh, H. Menke, P. M. R. Brydon, C. Timm, A. Ramires, and D. F. Agterberg, Stabilizing even-parity chiral superconductivity in Sr2RuO4, Phys. Rev. Res. 2, 032023 (2020).
  18. H. S. Røising, T. Scaffidi, F. Flicker, G. F. Lange, and S. H. Simon, Superconducting order of Sr2RuO4 from a three-dimensional microscopic model, Phys. Rev. Res. 1, 033108 (2019).
  19. S. Kittaka, S. Nakamura, T. Sakakibara, N. Kikugawa, T. Terashima, S. Uji, D. A. Sokolov, A. P. Mackenzie, K. Irie, Y. Tsutsumi et al., Searching for gap zeros in Sr2RuO4 via field-angle-dependent specific-heat measurement, J. Phys. Soc. Jpn. 87, 093703 (2018).
  20. Another even-parity state is, for instance, the superposition of extended s wave and d wave, for which we simply use the basis function Φs(k)=coskx+cosky.
  21. J. M. Luttinger and J. C. Ward, Ground-state energy of a many-fermion system. II, Phys. Rev. 118, 1417 (1960).
  22. J. Keller, K. Scharnberg, and H. Monien, Free energy of anisotropic superconductors, Physica C 152, 302 (1988).
  23. G. Bruls, D. Weber, B. Wolf, P. Thalmeier, B. Lüthi, A. de Visser, and A. Menovsky, Strain-Order-Parameter Coupling and Phase Diagrams in Superconducting UPt3, Phys. Rev. Lett. 65, 2294 (1990).
  24. R. H. Heffner, J. O. Willis, J. L. Smith, P. Birrer, C. Baines, F. N. Gygax, B. Hitti, E. Lippelt, H. R. Ott, A. Schenck, and D. E. MacLaughlin, Muon-spin relaxation studies of weak magnetic correlations in U1−xThxBe13, Phys. Rev. B 40, 806 (1989).
  25. E. R. Schemm, W. J. Gannon, C. M. Wishne, W. P. Halperin, and A. Kapitulnik, Observation of broken time-reversal symmetry in the heavy-fermion superconductor UPt3, Science 345, 190 (2014).
  26. V. P. Mineev and K. Samokhin, Introduction to Unconventional Superconductivity (Gordon and Breach, New York, 1999).
  27. T. Nomura, Theory of transport properties in the p-wave superconducting state of Sr2RuO4—A microscopic determination of the gap structure, J. Phys. Soc. Jpn. 74, 1818 (2005).

Outline

Information

Phys. Rev. Research 3, L012004– Published 14 January, 2021
  • Received 26 September 2020
  • Revised 6 December 2020
  • Accepted 11 December 2020
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation