Superconducting instability of a non-centrosymmetric system

Open Access
Regular Article


The Fermi gas approach to the weak-coupling superconductivity in the non-centrosymmetric systems lead to a conclusion of an approximately spin-orbit coupling independent critical temperature of the singlet states as well as the triplet states defined by the order parameter aligned with the antisymmetric spin-orbit coupling vector. We indicate that the above results follow from a simplified approximation of a density of states by a constant Fermi surface value. Such a scenario does not properly account for the spin-split quasiparticle energy spectrum and reduces the spin-orbit coupling influence on superconductivity to the bare pair-breaking effect of a lifted spin degeneracy. Applying the tight-binding model, which captures the primary features of the spin-split energy band, i.e., its enhanced width and the spin-orbit coupling induced redistribution of the spectral weights in the density of states, we calculate the critical temperature of a non-centrosymmetric superconductor. We report a general tendency of the critical temperature to be suppressed by the antisymmetric spin-orbit coupling. We indicate that, the monotonic decrease of the critical temperature may be altered by the spin-orbit coupling induced van Hove singularities which, when driven to the Fermi level, generate maxima in the phase diagram. Extending our considerations to the intermediate-coupling superconductivity we point out that the spin-orbit coupling induced change of the critical temperature depends on the structure of the electronic energy band and both – the strength and symmetry of the pair potential. Finally, we discuss the mixed singlet-triplet state superconducting instability and establish conditions concerning the symmetry of the singlet and triplet counterparts as well as the range of the spin-orbit coupling energy which make such a phase transition possible.


Solid State and Materials 


  1. 1.
    E. Bauer, G. Hilscher, H. Michor, C. Paul, E.W. Scheidt, A. Gribanov, Y. Seropegin, H. Noel, M. Sigrist, P. Rogl, Phys. Rev. Lett. 92, 027003 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    Non-centrosymmetric Superconductors, Introduction and Overview, edited by E. Bauer, M. Sigrist, Vol. 847 of Lecture Notes in Physics (Springer, Heidelberg, 2012)Google Scholar
  3. 3.
    Y.A. Bychkov, E.I. Rashba, J. Exp. Theor. Phys. Lett. 39, 78 (1984)Google Scholar
  4. 4.
    V.M. Edelstein, Zh. Eksp. Teor. Fiz. 95, 2151 (1989)Google Scholar
  5. 5.
    L.P. Gor’kov, E.I. Rashba, Phys. Rev. Lett. 87, 037004 (2001)ADSCrossRefGoogle Scholar
  6. 6.
    P.A. Frigeri, D.F. Agterberg, A. Koga, M. Sigrist, Phys. Rev. Lett. 92, 097001 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    V. Barzykin, L.P. Gor’kov, Phys. Rev. Lett. 89, 227002 (2002)ADSCrossRefGoogle Scholar
  8. 8.
    E. Bauer, R.T. Khan, H. Michor, E. Royanian, A. Grytsiv, N. Melnychenko-Koblyuk, P. Roghl, D. Reith, R. Podloucky, E.W. Scheidt et al., Phys. Rev. B 80, 064504 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    E. Bauer, G. Roghl, X.Q. Chen, R.T. Khan, H. Michor, G. Hilscher, E. Royanian, K. Kumagai, D.Z. Li, Y.Y. Li et al., Phys. Rev. B 82, 064511 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    K.V. Samokhin, E.S. Zijlstra, S.K. Bose, Phys. Rev. B 69, 094514 (2004)ADSCrossRefGoogle Scholar
  11. 11.
    M.J. Winiarski, M. Samsel-Czekała, Intermetallics 56, 44 (2015)CrossRefGoogle Scholar
  12. 12.
    E. Bauer, P. Rogl, Non-centrosymmetric Superconductors: Strong vs. Weak Electronic Correlations, Vol. 847 of Lecture Notes in Physics (2012), pp. 3–33Google Scholar
  13. 13.
    Y. Ōnuki, R. Settai, Electronic States and Superconducting Properties of Non-centrosymmetric Rare Earth Compounds, Vol. 847 of Lecture Notes in Physics (2012), pp. 81–126Google Scholar
  14. 14.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover Publications, INC., New York, 1975)Google Scholar
  15. 15.
    P.A. Frigeri, D.F. Agterberg, I. Milat, M. Sigrist, Eur. Phys. J. B 54, 435 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    Y. Tada, N. Kawakami, S. Fujimoto, New J. Phys. 11, 055070 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    T. Shibayama, M. Nohara, H.A. Katori, Y. Okamoto, Z. Hiori, H. Takagi, J. Phys. Soc. Jpn 76, 073708 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    A. Harada, N. Tamura, H. Mukuda, Y. Kitaoka, K. Wakui, S. Akutagawa, J. Akimitsu, J. Phys. Soc. Jpn 78, 025003 (2009)ADSCrossRefGoogle Scholar
  19. 19.
    S. Fujimoto, Bulletin Phys. Soc. Jpn 63, 20 (2008)Google Scholar
  20. 20.
    Y. Yanase, M. Sigrist, J. Phys. Soc. Jpn 76, 124709 (2007)ADSCrossRefGoogle Scholar
  21. 21.
    S.C. Zhang, Phys. Rev. Lett. 65, 120 (1990)ADSCrossRefGoogle Scholar
  22. 22.
    R.T. Scalettar, N.E. Bickers, D.J. Scalapino, Phys. Rev. Lett. 62, 1407 (1989)ADSCrossRefGoogle Scholar
  23. 23.
    M. Sigrist, K. Ueda, Rev. Mod. Phys. 63, 239 (1991)ADSCrossRefGoogle Scholar
  24. 24.
    I.A. Sergienko, S.H. Curnoe, Phys. Rev. B 70, 214510 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    T. Takimoto, P. Thalmeier, J. Phys. Soc. Jpn 78, 103703 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    T. Yokoyama, S. Onari, Y. Tanaka, Phys. Rev. B 75, 172511 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    Y. Levi, O. Millo, A. Sharoni, Y. Tsabba, G. Leitus, S. Reich, Europhys. Lett. 51, 564 (2000)ADSCrossRefGoogle Scholar
  28. 28.
    T. Nishio, T. An, A. Nomura, K. Miyachi, T. Eguchi, H. Sakata, S. Lin, N. Hayashi, N. Nakai, M. Machida et al., Phys. Rev. Lett. 101, 167001 (2008)ADSCrossRefGoogle Scholar
  29. 29.
    P. Das, C.V. Tomy, S.S. Banerjee, H. Takeya, S. Ramakrishnan, A.K. Grover, Phys. Rev. B 78, 214504 (2008)ADSCrossRefGoogle Scholar
  30. 30.
    S. LaShell, B.A. McDougall, E. Jensen, Phys. Rev. Lett. 77, 3419 (1996)ADSCrossRefGoogle Scholar
  31. 31.
    L. Petersen, P.T. Sprunger, P. Hofmann, E. Lægsgaard, B.G. Briner, M. Doering, H.P. Rust, A.M. Bradshaw, F. Besenbacher, E.W. Plummer, Phys. Rev. B 57, R6858 (1998)ADSCrossRefGoogle Scholar
  32. 32.
    E. Rotenberg, J.W. Chung, S.D. Kevan, Phys. Rev. Lett. 82, 4066 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    N. Reyren, S. Thiel, A.D. Caviglia, L.F. Kourkoutis, G. Hammerl, C. Richter, C.W. Schneider, T. Kopp, A.S. Ruetschi, D. Jaccard et al., Science 317, 1196 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    E. Bauer, Superconductivity in materials without inversion symmetry (Karpacz Winter School of Theoretical Physics, 2014)Google Scholar

Copyright information

© The Author(s) 2017

Open Access This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of Quantum TechnologiesFaculty of Fundamental Problems of Technology, Wrocław University of Science and TechnologyWrocławPoland

Personalised recommendations