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Testing the Fully Gapped s-Wave Superconductor \(\hbox {CeCu}_2\hbox {Si}_2\) by Impurity-Induced Intra-gap States

  • Dongdong Wang
  • Bin LiuEmail author
Article
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Abstract

The fully gapped s-wave superconducting state, such as nodeless \(s^{\pm }\)-wave and \(s^{++}\)-wave, was proposed by recent experiments in the multiband superconductor \(\hbox {CeCu}_{2}\hbox {Si}_{2}\). In this paper, we study the problem within an effective two hybridization bands model obtained from the first principle calculations. Our results based on T-matrix approximation reveal that for \(s^{++}\)-wave pairing, there are no intra-gap resonance states induced by a nonmagnetic impurity irrespective of the inter-band impurity scattering strength. However, in the case of sign-changing \(s^{\pm }\)-wave pairing, we find two intra-gap resonance states appearing at positive and negative energies around the Fermi energy with introducing inter-band impurity scattering. These features can be readily verified by scanning tunneling microscopy/spectroscopy and are proposed to identify the sign-changing fully gapped superconducting state in \(\hbox {CeCu}_{2}\hbox {Si}_{2}\) at ambient pressure.

Keywords

Heavy-fermion superconductivity Gap symmetry Nonmagnetic impurity effect 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant No. 11774025.

References

  1. 1.
    F. Steglich, J. Aarts, C.D. Bredl, W. Lieke, D. Meschede, W. Franz, H. Schäfer, Phys. Rev. Lett. 43, 1892 (1979)ADSCrossRefGoogle Scholar
  2. 2.
    B. Bellarbi, A. Benoit, D. Jaccard, J.M. Mignot, H.F. Braun, Phys. Rev. B 30, 1182 (1984)ADSCrossRefGoogle Scholar
  3. 3.
    F. Thomas, J. Thomasson, C. Ayache, C. Geibel, F. Steglich, Physica B 186–188, 303 (1993)CrossRefGoogle Scholar
  4. 4.
    G. Seyfarth, A.S. Retschi, K. Sengupta, A. Georges, D. Jaccard, Europhys. Lett. 98, 17012 (2012)ADSCrossRefGoogle Scholar
  5. 5.
    G. Seyfarth, A.S. Retschi, K. Sengupta, A. Georges, D. Jaccard, S. Watanabe, K. Miyake, Phys. Rev. B 85, 205105 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    A.T. Holmes, D. Jaccard, K. Miyake, J. Phys. Soc. Jpn. 76, 051002 (2007)ADSCrossRefGoogle Scholar
  7. 7.
    Y. Onishi, K. Miyake, J. Phys. Soc. Jpn. 69, 3955 (2000)ADSCrossRefGoogle Scholar
  8. 8.
    J.P. Rueff, S. Raymond, M. Taguchi, M. Sikora, J.P. Iti, F. Baudelet, D. Braithwaite, G. Knebel, D. Jaccard, Phys. Rev. Lett. 106, 186405 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    K. Miyake, J. Phys. Condens. Matter 19, 125201 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    E. Lengyel, M. Nicklas, H.S. Jeevan, C. Geibel, F. Steglich, Phys. Rev. Lett. 107, 057001 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    O. Stockert, J. Arndt, E. Faulhaber, C. Geibel, H.S. Jeevan, S. Kirchner, M. Loewenhaupt, K. Schmalzl, W. Schmidt, Q. Si, F. Steglich, Nat. Phys. 7, 119 (2011)CrossRefGoogle Scholar
  12. 12.
    H.Q. Yuan, F.M. Grosche, M. Deppe, C. Geibel, G. Sparn, F. Steglich, Science 302, 2104 (2003)ADSCrossRefGoogle Scholar
  13. 13.
    M. Nicklas, G. Sparn, R. Lackner, E. Bauer, F. Steglich, Physica B 359–361, 386 (2005)CrossRefGoogle Scholar
  14. 14.
    K. Ueda, Y. Kitaoka, H. Yamada, Y. Kohori, T. Kohara, K. Asayama, J. Phys. Soc. Jpn. 56, 867 (1987)ADSCrossRefGoogle Scholar
  15. 15.
    Y. Kitaoka, K. Ueda, K. Fujiwara, H. Arimoto, H. Iida, K. Asayama, J. Phys. Soc. Jpn. 55, 723 (1986)ADSCrossRefGoogle Scholar
  16. 16.
    K. Fujiwara, Y. Hata, K. Kobayashi, K. Miyoshi, J. Takeuchi, Y. Shimaoka, H. Kotegawa, T.C. Kobayashi, C. Geibel, F. Steglich, J. Phys. Soc. Jpn. 77, 123711 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    C. Bredl, H. Spille, U. Rauchschwalbe, W. Lieke, F. Steglich, G. Cordier, W. Assmus, M. Herrmann, J. Aarts, J. Magn. Magn. Mater. 31, 373 (1983)ADSCrossRefGoogle Scholar
  18. 18.
    J. Arndt, O. Stockert, K. Schmalzl, E. Faulhaber, H.S. Jeevan, C. Geibel, W. Schmidt, M. Loewenhaupt, F. Steglich, Phys. Rev. Lett. 106, 246401 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    S. Kittaka, Y. Aoki, Y. Shimura, T. Sakakibara, S. Seiro, C. Geibel, F. Steglich, H. Ikeda, K. Machida, Phys. Rev. Lett. 112, 067002 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    M. Enayat, Z. Sun, A. Maldonado, H. Suderow, S. Seiro, C. Geibel, S. Wirth, F. Steglich, P. Wahl, Phys. Rev. B 93, 045123 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    G.M. Pang, M. Smidman, J.L. Zhang, L. Jiao, Z.F. Weng, E.M. Nica, Y. Chen, W.B. Jiang, Y.J. Zhang, H.S. Jeevan, P. Gegenwart, F. Steglich, Q. Si, H.Q. Yuan, PNAS 115, 5343–5347 (2018)ADSCrossRefGoogle Scholar
  22. 22.
    T. Takenaka, Y. Mizukami, J.A. Wilcox, M. Konczykowski, S. Seiro, C. Geibel, Y. Tokiwa, Y. Kasahara, C. Putzke, Y. Matsuda, A. Carrington, T. Shibauchi, Phys. Rev. Lett. 119, 077001 (2017)ADSCrossRefGoogle Scholar
  23. 23.
    Y. Li, M. Liu, Z. Fu, X. Chen, F. Yang, Y.F. Yang, Phys. Rev. Lett. 120, 217001 (2018)ADSCrossRefGoogle Scholar
  24. 24.
    T. Yamashita, T. Takenaka, Y. Tokiwa, J.A. Wilcox, Y. Mizukami, D. Terazawa, Y. Kasahara, S. Kittaka, T. Sakakibara, M. Konczykowski, S. Seiro, H.S. Jeevan, C. Geibel, C. Putzke, T. Onishi, H. Ikeda, A. Carrington, T. Shibauchi, Y. Matsuda, Sci. Adv. 3, e1601667 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    H. Ikeda, M. Suzuki, R. Arita, Phys. Rev. Lett. 114, 147003 (2015)ADSCrossRefGoogle Scholar
  26. 26.
    P. Aynajian, E.H. da Silva Neto, A. Gyenis, R.E. Baumbach, J.D. Thompson, Z. Fisk, E.D. Bauer, A. Yazdani, Nature 486, 201 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    M.P. Allan, F. Massee, D.K. Morr, J. van Dyke, A.W. Rost, A.P. Mackenzie, C. Petrovic, J.C. Davis, Nat. Phys. 9, 468 (2013)CrossRefGoogle Scholar
  28. 28.
    B.B. Zhou, S. Misra, E.H. da Silva Neto, P. Aynajian, R.E. Baumbach, J.D. Thompson, E.D. Bauer, A. Yazdani, Nat. Phys. 9, 474 (2013)CrossRefGoogle Scholar
  29. 29.
    B. Liu, Phys. Rev. B 88, 245127 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    G. Zhang, B. Liu, Y.F. Yang, S. Feng, Front. Phys. 11, 117402 (2016)CrossRefGoogle Scholar
  31. 31.
    A.V. Balatsky, I. Vekhter, J.-X. Zhu, Rev. Mod. Phys. 78, 373 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    B. Liu, Y. Liang, Phys. Rev. B 77, 245121 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    B. Liu, Phys. Rev. B 79, 172501 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    B. Liu, I. Eremin, Phys. Rev. B 78, 014518 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    B. Liu, X. Hu, Phys. Rev. B 81, 144504 (2010)ADSCrossRefGoogle Scholar
  36. 36.
    B. Liu, S. Feng, Europhys. Lett. 106, 17003 (2013)ADSCrossRefGoogle Scholar
  37. 37.
    D.D. Wang, B. Liu, M. Liu, Y.F. Yang, S. Feng, Front. Phys. 14, 013501 (2019)CrossRefGoogle Scholar
  38. 38.
    M. Matsumoto, K. Mikito, K. Hiroaki, J. Phys. Soc. Jpn. 78(4), 084718 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    P.W. Anderson, J. Phys. Chem. Solids 11, 26 (1959)ADSCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Jiaotong UniversityBeijingChina

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