- Letter
- Open Access
Proposal for identifying possible even-parity superconducting states in using planar tunneling spectroscopy
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 -wave, -wave, and -wave states—have emerged as leading candidates for the superconducting states of . 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/ junctions with various angles between the junction interface and the crystal axis of the . 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 .
Physics Subject Headings (PhySH)
Article Text
Supplemental Material
References (59)
- A. P. Mackenzie and Y. Maeno, The superconductivity of and the physics of spin-triplet pairing, Rev. Mod. Phys. 75, 657 (2003).
- C. Kallin and A. J. Berlinsky, Is a chiral -wave superconductor?, J. Phys.: Condens. Matter, 21, 164210 (2009).
- A. P. Mackenzie, T. Scaffidi, C. W. Hicks, and Y. Maeno, Even odder after twenty-three years: The superconducting order parameter puzzle of , npj Quantum Mater. 2, 40 (2017).
- 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).
- 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 from oxygen-17 nuclear magnetic resonance, Nature (London) 574, 72 (2019).
- K. Ishida, M. Manago, and Y. Maeno, Reduction of the Knight shift in the superconducting state and the heat-up effect by NMR pulses on , J. Phys. Soc. Jpn. 89, 034712 (2020).
- 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 , Proc. Natl. Acad. Sci. USA 118, e2025313118 (2021).
- 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 Observed by Polarized Neutron Scattering, Phys. Rev. Lett. 125, 217004 (2020).
- H. G. Suh, H. Menke, P. M. R. Brydon, C. Timm, A. Ramires, and D. F. Agterberg, Stabilizing even-parity chiral superconductivity in , Phys. Rev. Research 2, 032023(R) (2020).
- S. A. Kivelson, A. C. Yuan, B. Ramshaw, and R. Thomale, A proposal for reconciling diverse experiments on the superconducting state in , npj Quantum Mater. 5, 43 (2020).
- 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).
- 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 , Nat. Phys. 17, 194 (2021).
- 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 , Nat. Phys. 17, 199 (2021).
- 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 under stress, Nat. Phys. 17, 748 (2021).
- 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 , Nature (London) 394, 558 (1998).
- J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and A. Kapitulnik, High Resolution Polar Kerr Effect Measurements of : Evidence for Broken Time-Reversal Symmetry in the Superconducting State, Phys. Rev. Lett. 97, 167002 (2006).
- 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).
- 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) surfaces, Phys. Rev. B 55, R14757 (1997).
- J. Y. T. Wei, N.-C. Yeh, D. F. Garrigus, and M. Strasik, Directional Tunneling and Andreev Reflection on Single Crystals: Predominance of -Wave Pairing Symmetry Verified with the Generalized Blonder, Tinkham, and Klapwijk Theory, Phys. Rev. Lett. 81, 2542 (1998).
- I. Iguchi, W. Wang, M. Yamazaki, Y. Tanaka, and S. Kashiwaya, Angle-resolved Andreev bound states in anisotropic -wave high- superconductors, Phys. Rev. B 62, R6131 (2000).
- S. Kashiwaya and Y. Tanaka, Tunnelling effects on surface bound states in unconventional superconductors, Rep. Prog. Phys. 63, 1641 (2000).
- F. Laube, G. Boll, H. v. Löhneysen, M. Fogelström, and F. Lichtenberg, Spin-Triplet Superconductivity in Probed by Andreev Reflection, Phys. Rev. Lett. 84, 1595 (2000).
- M. D. Upward, L. P. Kouwenhoven, A. F. Morpurgo, N. Kikugawa, Z. Q. Mao, and Y. Maeno, Direct observation of the superconducting gap of , Phys. Rev. B 65, 220512(R) (2002).
- H. Suderow, V. Crespo, I. Guillamon, S. Vieira, F. Servant, P. Lejay, J. P. Brison, and J. Flouquet, A nodeless superconducting gap in from tunneling spectroscopy, New J. Phys. 11, 093004 (2009).
- H. Kambara, S. Kashiwaya, H. Kashiwaya, Y. Tanaka, and Y. Maeno, Local transport characteristics of break junction in microbridge, Physica C (Amsterdam, Neth.) 471, 708 (2011).
- S. Kashiwaya, H. Kashiwaya, H. Kambara, T. Furuta, H. Yaguchi, Y. Tanaka, and Y. Maeno, Edge States of Detected by In-Plane Tunneling Spectroscopy, Phys. Rev. Lett. 107, 077003 (2011).
- K. Yada, A. A. Golubov, Y. Tanaka, and S. Kashiwaya, Microscopic Theory of Tunneling Spectroscopy in , J. Phys. Soc. Jpn. 88, 074706 (2014).
- 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 , Phys. Rev. B 88, 134521 (2013).
- H. Wang, W. Lou, J. Luo, J. Wei, Y. Liu, J. E. Ortmann, and Z. Q. Mao, Enhanced superconductivity at the interface of W/ point contacts, Phys. Rev. B 91, 184514 (2015).
- H. Wang, J. Luo, W. Lou, J. E. Ortmann, Z. Q. Mao, Y. Liu, and J. Wei, Probing chiral superconductivity in underneath the surface by point contact measurements, New J. Phys. 19, 053001 (2017).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.3.L032062 for demonstrating the differential conductance with different and . We also discuss the differential conductance of -wave, nematic -wave, and spin-triplet helical -wave states.
- 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).
- C. Bruder, Andreev scattering in anisotropic superconductors, Phys. Rev. B 41, 4017 (1990).
- Y. Tanaka and S. Kashiwaya, Theory of Tunneling Spectroscopy of -Wave Superconductors, Phys. Rev. Lett. 74, 3451 (1995).
- S. Kashiwaya, Y. Tanaka, M. Koyanagi, and K. Kajimura, Theory for tunneling spectroscopy of anisotropic superconductors, Phys. Rev. B 53, 2667 (1996).
- K. Sengupta, H.-J. Kwon, and V. M. Yakovenko, Edge states and determination of pairing symmetry in superconducting , Phys. Rev. B 65, 104504 (2002).
- K. Deguchi, Z. Q. Mao, H. Yaguchi, and Y. Maeno, Gap Structure of the Spin-Triplet Superconductor Determined from the Field-Orientation Dependence of the Specific Heat, Phys. Rev. Lett. 92, 047002 (2004).
- 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 from quasiparticle interference imaging, Proc. Natl. Acad. Sci. USA 117, 5222 (2020).
- 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 , Europhys. Lett. 104, 17013 (2013).
- T. Scaffidi and S. H. Simon, Large Chern Number and Edge Currents in , Phys. Rev. Lett. 115, 087003 (2015).
- I. I. Mazin and D. J. Singh, Ferromagnetic Spin Fluctuation Induced Superconductivity in , Phys. Rev. Lett. 79, 733 (1997).
- O. Chmaissem, J. D. Jorgensen, H. Shaked, S. Ikeda, and Y. Maeno, Thermal expansion and compressibility of , Phys. Rev. B 57, 5067 (1998).
- L. J. Buchholtz and G. Zwicknagl, Identification of -wave superconductors, Phys. Rev. B 23, 5788 (1981).
- C.-R. Hu, Midgap Surface States as a Novel Signature for -Wave Superconductivity, Phys. Rev. Lett. 72, 1526 (1994).
- Y. Asano, Y. Tanaka, and S. Kashiwaya, Phenomenological theory of zero-energy Andreev resonant states, Phys. Rev. B 69, 134501 (2004).
- S. Kobayashi, Y. Tanaka, and M. Sato, Fragile surface zero-energy flat bands in three-dimensional chiral superconductors, Phys. Rev. B 92, 214514 (2015).
- 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).
- S.-S. Suzuki, M. Sato, and Y. Tanaka, Identifying possible pairing states in by tunneling spectroscopy, Phys. Rev. B 101, 054505 (2020).
- 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 under hydrostatic pressure and disorder, Nat. Commun. 12, 3920 (2021).
- 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 under uniaxial pressure, Proc. Natl. Acad. Sci. USA 118, e2020492118 (2021).
- S. Kashiwaya, K. Saitoh, H. Kashiwaya, M. Koyanagi, M. Sato, K. Yada, Y. Tanaka, and Y. Maeno, Time-reversal invariant superconductivity of revealed by Josephson effects, Phys. Rev. B 100, 094530 (2019).
- H. S. Røising, T. Scaffidi, F. Flicker, G. F. Lange, and S. H. Simon, Superconducting order of from a three-dimensional microscopic model, Phys. Rev. Research 1, 033108 (2019).
- P. G. Björnsson, Y. Maeno, M. E. Huber, and K. A. Moler, Scanning magnetic imaging of , Phys. Rev. B 72, 012504 (2005).
- 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 , Phys. Rev. B 76, 014526 (2007).
- P. J. Baker, R. J. Ormeno, C. E. Gough, Z. Q. Mao, S. Nishizaki, and Y. Maeno, Microwave surface impedance measurements of : The effect of impurities, Phys. Rev. B 80, 115126 (2009).
- 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 -wave superconductor, Phys. Rev. B 98, 134508 (2018).
- V. L. Berezinskii, New model of the anisotropic phase of superfluid , Pis'ma Zh. Éksp. Teor. Fiz. 20, 628 (1974) [JETP Lett. 20, 287 (1974)].
- 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).
- J. Linder and A. V. Balatsky, Odd-frequency superconductivity, Rev. Mod. Phys. 91, 045005 (2019).