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  • Letter
  • Open Access

Proposal for identifying possible even-parity superconducting states in Sr2RuO4 using planar tunneling spectroscopy

Satoshi Ikegaya1,2, Shu-Ichiro Suzuki2, Yukio Tanaka2, and Dirk Manske1

  • 1Max-Planck-Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany
  • 2Department of Applied Physics, Nagoya University, Nagoya 464-8603, Japan

Phys. Rev. Research 3, L032062 – Published 13 September, 2021

DOI: https://doi.org/10.1103/PhysRevResearch.3.L032062

Abstract

After more than 25 years of research, three even-parity superconducting states—the d+id-wave, d+ig-wave, and s+id-wave states—have emerged as leading candidates for the superconducting states of Sr2RuO4. In the present work, we propose a tunneling spectroscopy experiment for distinguishing among these three superconducting states. The key component of our proposal is that we examine the conductance spectra of normal-metal/Sr2RuO4 junctions with various angles between the junction interface and the crystal axis of the Sr2RuO4. The angle dependence of the conductance spectra shows a unique pattern in each superconducting state, which can function as a fingerprint for verifying the pairing symmetry of Sr2RuO4.

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References (59)

  1. A. P. Mackenzie and Y. Maeno, The superconductivity of Sr2RuO4 and the physics of spin-triplet pairing, Rev. Mod. Phys. 75, 657 (2003).
  2. C. Kallin and A. J. Berlinsky, Is Sr2RuO4 a chiral p-wave superconductor?, J. Phys.: Condens. Matter, 21, 164210 (2009).
  3. A. P. Mackenzie, T. Scaffidi, C. W. Hicks, and Y. Maeno, Even odder after twenty-three years: The superconducting order parameter puzzle of Sr2RuO4, npj Quantum Mater. 2, 40 (2017).
  4. Y. Maeno, H. Hashimoto, K. Yoshida, S. Nishizaki, T. Fujita, J. G. Bednorz, and F. Lichtenberg, Superconductivity in a layered perovskite without copper, Nature (London) 372, 532 (1994).
  5. A. Pustogow, Y. Luo, A. Chronister, Y.-S. Su, D. A. Sokolov, F. Jerzembeck, A. P. Mackenzie, C. W. Hicks, N. Kikugawa, S. Raghu, E. D. Bauer, and S. E. Brown, Constraints on the superconducting order parameter in Sr2RuO4 from oxygen-17 nuclear magnetic resonance, Nature (London) 574, 72 (2019).
  6. K. Ishida, M. Manago, 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, Proc. Natl. Acad. Sci. USA 118, e2025313118 (2021).
  8. A. N. Petsch, M. Zhu, M. Enderle, Z. Q. Mao, Y. Maeno, I. I. Mazin, and S. M. Hayden, Reduction of the Spin Susceptibility in the Superconducting State of Sr2RuO4 Observed by Polarized Neutron Scattering, Phys. Rev. Lett. 125, 217004 (2020).
  9. 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. Research 2, 032023(R) (2020).
  10. 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).
  11. J. Clepkens, A. W. Lindquist, and H.-Y. Kee, Shadowed triplet pairings in Hund's metals with spin-orbit coupling, Phys. Rev. Research 3, 013001 (2021).
  12. S. Benhabib, C. Lupien, I. Paul, L. Berges, M. Dion, M. Nardone, A. Zitouni, Z. Q. Mao, Y. Maeno, A. Georges, L. Taillefer, and C. Proust, Ultrasound evidence for a two-component superconducting order parameter in Sr2RuO4, Nat. Phys. 17, 194 (2021).
  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. 17, 199 (2021).
  14. V. Grinenko, S. Ghosh, R. Sarkar, J.-C. Orain, A. Nikitin, M. Elender, D. Das, Z. Guguchia, F. Brückner, M. E. Barber, J. Park, N. Kikugawa, D. A. Sokolov, J. S. Bobowski, T. Miyoshi, Y. Maeno, A. P. Mackenzie, H. Luetkens, C. W. Hicks, and H.-H. Klauss, Split superconducting and time-reversal symmetry-breaking transitions in Sr2RuO4 under stress, Nat. Phys. 17, 748 (2021).
  15. G. M. Luke, Y. Fudamoto, K. M. Kojima, M. I. Larkin, J. Merrin, B. Nachumi, Y. J. Uemura, Y. Maeno, Z. Q. Mao, Y. Mori, H. Nakamura, and M. Sigrist, Time-reversal symmetry-breaking superconductivity in Sr2RuO4, Nature (London) 394, 558 (1998).
  16. 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).
  17. S. Kashiwaya, M. Koyanagi, M. Matsuda, and K. Kajimura, Study of zero-bias conductance peaks in YBCO films by LT-STM, Physica B (Amsterdam, Neth.) 194-196, 2119 (1994).
  18. L. Alff, H. Takashima, S. Kashiwaya, N. Terada, H. Ihara, Y. Tanaka, M. Koyanagi, and K. Kajimura, Spatially continuous zero-bias conductance peak on (110) YBa2Cu3O7−δ surfaces, Phys. Rev. B 55, R14757 (1997).
  19. J. Y. T. Wei, N.-C. Yeh, D. F. Garrigus, and M. Strasik, Directional Tunneling and Andreev Reflection on YBa2Cu3O7−δ Single Crystals: Predominance of d-Wave Pairing Symmetry Verified with the Generalized Blonder, Tinkham, and Klapwijk Theory, Phys. Rev. Lett. 81, 2542 (1998).
  20. I. Iguchi, W. Wang, M. Yamazaki, Y. Tanaka, and S. Kashiwaya, Angle-resolved Andreev bound states in anisotropic d-wave high-TcYBa2Cu3O7−y superconductors, Phys. Rev. B 62, R6131 (2000).
  21. S. Kashiwaya and Y. Tanaka, Tunnelling effects on surface bound states in unconventional superconductors, Rep. Prog. Phys. 63, 1641 (2000).
  22. F. Laube, G. Boll, H. v. Löhneysen, M. Fogelström, and F. Lichtenberg, Spin-Triplet Superconductivity in Sr2RuO4 Probed by Andreev Reflection, Phys. Rev. Lett. 84, 1595 (2000).
  23. M. D. Upward, L. P. Kouwenhoven, A. F. Morpurgo, N. Kikugawa, Z. Q. Mao, and Y. Maeno, Direct observation of the superconducting gap of Sr2RuO4, Phys. Rev. B 65, 220512(R) (2002).
  24. H. Suderow, V. Crespo, I. Guillamon, S. Vieira, F. Servant, P. Lejay, J. P. Brison, and J. Flouquet, A nodeless superconducting gap in Sr2RuO4 from tunneling spectroscopy, New J. Phys. 11, 093004 (2009).
  25. H. Kambara, S. Kashiwaya, H. Kashiwaya, Y. Tanaka, and Y. Maeno, Local transport characteristics of break junction in Sr2RuO4 microbridge, Physica C (Amsterdam, Neth.) 471, 708 (2011).
  26. S. Kashiwaya, H. Kashiwaya, H. Kambara, T. Furuta, H. Yaguchi, Y. Tanaka, and Y. Maeno, Edge States of Sr2RuO4 Detected by In-Plane Tunneling Spectroscopy, Phys. Rev. Lett. 107, 077003 (2011).
  27. K. Yada, A. A. Golubov, Y. Tanaka, and S. Kashiwaya, Microscopic Theory of Tunneling Spectroscopy in Sr2RuO4, J. Phys. Soc. Jpn. 88, 074706 (2014).
  28. I. A. Firmo. S. Lederer, C. Lupien, A. P. Mackenzie, J. C. Davis, and S. A. Kivelson, Evidence from tunneling spectroscopy for a quasi-one-dimensional origin of superconductivity in Sr2RuO4, Phys. Rev. B 88, 134521 (2013).
  29. H. Wang, W. Lou, J. Luo, J. Wei, Y. Liu, J. E. Ortmann, and Z. Q. Mao, Enhanced superconductivity at the interface of W/Sr2RuO4 point contacts, Phys. Rev. B 91, 184514 (2015).
  30. H. Wang, J. Luo, W. Lou, J. E. Ortmann, Z. Q. Mao, Y. Liu, and J. Wei, Probing chiral superconductivity in Sr2RuO4 underneath the surface by point contact measurements, New J. Phys. 19, 053001 (2017).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032062 for demonstrating the differential conductance with different kFN and z0. We also discuss the differential conductance of dx2−y2-wave, nematic dxz-wave, and spin-triplet helical p-wave states.
  32. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982).
  33. C. Bruder, Andreev scattering in anisotropic superconductors, Phys. Rev. B 41, 4017 (1990).
  34. Y. Tanaka and S. Kashiwaya, Theory of Tunneling Spectroscopy of d-Wave Superconductors, Phys. Rev. Lett. 74, 3451 (1995).
  35. S. Kashiwaya, Y. Tanaka, M. Koyanagi, and K. Kajimura, Theory for tunneling spectroscopy of anisotropic superconductors, Phys. Rev. B 53, 2667 (1996).
  36. K. Sengupta, H.-J. Kwon, and V. M. Yakovenko, Edge states and determination of pairing symmetry in superconducting Sr2RuO4, Phys. Rev. B 65, 104504 (2002).
  37. K. Deguchi, Z. Q. Mao, H. Yaguchi, and Y. Maeno, Gap Structure of the Spin-Triplet Superconductor Sr2RuO4 Determined from the Field-Orientation Dependence of the Specific Heat, Phys. Rev. Lett. 92, 047002 (2004).
  38. R. Sharma, S. D. Edkins, Z. Wang, A. Kostin, C. Sow, Y. Maeno, A. P. Mackenzie, J. C. S. Davis, and V. Madhaven, Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging, Proc. Natl. Acad. Sci. USA 117, 5222 (2020).
  39. Q. H. Wang, C. Platt, Y. Yang, C. Honerkamp, F. C. Zhang, W. Hanke, T. M. Rice, and R. Thomale, Theory of superconductivity in a three-orbital model of Sr2RuO4, Europhys. Lett. 104, 17013 (2013).
  40. T. Scaffidi and S. H. Simon, Large Chern Number and Edge Currents in Sr2RuO4, Phys. Rev. Lett. 115, 087003 (2015).
  41. I. I. Mazin and D. J. Singh, Ferromagnetic Spin Fluctuation Induced Superconductivity in Sr2RuO4, Phys. Rev. Lett. 79, 733 (1997).
  42. O. Chmaissem, J. D. Jorgensen, H. Shaked, S. Ikeda, and Y. Maeno, Thermal expansion and compressibility of Sr2RuO4, Phys. Rev. B 57, 5067 (1998).
  43. L. J. Buchholtz and G. Zwicknagl, Identification of p-wave superconductors, Phys. Rev. B 23, 5788 (1981).
  44. C.-R. Hu, Midgap Surface States as a Novel Signature for dxa2−xb2-Wave Superconductivity, Phys. Rev. Lett. 72, 1526 (1994).
  45. Y. Asano, Y. Tanaka, and S. Kashiwaya, Phenomenological theory of zero-energy Andreev resonant states, Phys. Rev. B 69, 134501 (2004).
  46. S. Kobayashi, Y. Tanaka, and M. Sato, Fragile surface zero-energy flat bands in three-dimensional chiral superconductors, Phys. Rev. B 92, 214514 (2015).
  47. S. Tamura, S. Kobayashi, L. Bo, and Y. Tanaka, Theory of surface Andreev bound states and tunneling spectroscopy in three-dimensional chiral superconductors, Phys. Rev. B 95, 104511 (2017).
  48. S.-S. Suzuki, M. Sato, and Y. Tanaka, Identifying possible pairing states in Sr2RuO4 by tunneling spectroscopy, Phys. Rev. B 101, 054505 (2020).
  49. V. Grinenko, D. Das, R. Gupta, B. Zinkl, N. Kikugawa, Y. Maeno, C. W. Hicks, H.-H. Klauss, M. Sigrist, and R. Khasanov, Unsplit superconducting and time reversal symmetry breaking transitions in Sr2RuO4 under hydrostatic pressure and disorder, Nat. Commun. 12, 3920 (2021).
  50. Y.-S. Li, N. Kikugawa, D. A. Sokolov, F. Jerzembeck, A. S. Gibbs, Y. Maeno, C. W. Hicks, J. Schmalian, M. Nicklas, and A. P. Mackenzie, High-sensitivity heat-capacity measurements on Sr2RuO4 under uniaxial pressure, Proc. Natl. Acad. Sci. USA 118, e2020492118 (2021).
  51. S. Kashiwaya, K. Saitoh, H. Kashiwaya, M. Koyanagi, M. Sato, K. Yada, Y. Tanaka, and Y. Maeno, Time-reversal invariant superconductivity of Sr2RuO4 revealed by Josephson effects, Phys. Rev. B 100, 094530 (2019).
  52. 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. Research 1, 033108 (2019).
  53. P. G. Björnsson, Y. Maeno, M. E. Huber, and K. A. Moler, Scanning magnetic imaging of Sr2RuO4, Phys. Rev. B 72, 012504 (2005).
  54. J. R. Kirtley, C. Kallin, C. W. Hicks, E.-A. Kim, Y. Liu, K. A. Moler, Y. Maeno, and K. D. Nelson, Upper limit on spontaneous supercurrents in Sr2RuO4, Phys. Rev. B 76, 014526 (2007).
  55. P. J. Baker, R. J. Ormeno, C. E. Gough, Z. Q. Mao, S. Nishizaki, and Y. Maeno, Microwave surface impedance measurements of Sr2RuO4: The effect of impurities, Phys. Rev. B 80, 115126 (2009).
  56. S. V. Bakurskiy, Ya. V. Fominov, A. F. Shevchun, Y. Asano, Y. Tanaka, M. Yu. Kupriyanov, A. A. Golubov, M. R. Trunin, H. Kashiwaya, S. Kashiwaya, and Y. Maeno, Local impedance on a rough surface of a chiral p-wave superconductor, Phys. Rev. B 98, 134508 (2018).
  57. V. L. Berezinskii, New model of the anisotropic phase of superfluid He3, Pis'ma Zh. Éksp. Teor. Fiz. 20, 628 (1974) [JETP Lett. 20, 287 (1974)].
  58. Y. Tanaka, M. Sato, and N. Nagaosa, Symmetry and topology in superconductors: Odd-frequency pairing and edge states, J. Phys. Soc. Jpn. 81, 011013 (2012).
  59. J. Linder and A. V. Balatsky, Odd-frequency superconductivity, Rev. Mod. Phys. 91, 045005 (2019).

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