Skip to main content
SpringerLink
Log in

Topological objects in two-gap superconductor

  • Solid State and Materials
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We discuss the non-Abelian topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. We prove that these non-Abrikosov vortices can have either integral or fractional magnetic flux, depending on the interaction potential. We show that they are described by the non-Abelian topology π2(S 2) and π1(S 1), in addition to the well-known Abelian topology π1(S 1). Furthermore, we discuss the possibility to construct a stable magnetic knot in two-gap superconductor by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology π3(S 2) is described by the Chern-Simon index of the electromagnetic potential. We argue that similar topological objects may exist in multi-gap or multi-layer superconductors and multi-component Bose-Einstein condensates and superfluids, and discuss how these topological objects can be constructed in MgB2, Sr2RuO4, 3He, and liquid metallic hydrogen.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. P.A.M. Dirac, Proc. Roy. Soc. A 113, 60 (1931); P.A.M. Dirac, Phys. Rev. 74, 817 (1948)

    ADS  Google Scholar 

  2. A. Abrikosov, Sov. Phys. JETP 5, 1174 (1957); H. Nielsen, P. Olesen, Nucl. Phys. 61, 45 (1973)

    Google Scholar 

  3. T.H.R. Skyrme, Proc. Roy. Soc. (London) 260, 127 (1961); T.H.R. Skyrme, Proc. Roy. Soc. 262, 237 (1961); T.H.R. Skyrme, Nucl. Phys. 31, 556 (1962)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  4. L. Faddeev, A. Niemi, Nature 387, 58 (1997); J. Gladikowski, M. Hellmund, Phys. Rev. D 56, 5194 (1997); R. Battye, P. Sutcliffe, Phys. Rev. Lett. 81, 4798 (1998)

    Article  ADS  Google Scholar 

  5. Y.M. Cho, Phys. Rev. Lett. 87, 252001 (2001)

    Article  ADS  Google Scholar 

  6. Y.M. Cho, Phys. Lett. B 603, 88 (2004); Y.M. Cho, B.S. Park, P. Zhang, Int. J. Mod. Phys. A 23, 267 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  7. C. Myatt et al., Phys. Rev. Lett. 78, 586 (1997); D. Stamper-Kurn et al., Phys. Rev. Lett. 80, 2027 (1998)

    Article  ADS  Google Scholar 

  8. J. Nagamatsu et al., Nature 410, 63 (2001); S.L. Bud’ko et al., Phys. Rev. Lett. 86, 1877 (2001); C.U. Jung et al., Appl. Phys. Lett. 78, 4157 (2001)

    Article  ADS  Google Scholar 

  9. Y.M. Cho, e-print arXiv:cond-mat/0112325; Int. J. Pure Appl. Phys. 1, 246 (2005); Y.M. Cho, N.S. Yong, e-print arXiv: cond-mat/0308182, Int. J. Pure Appl. Phys. 2, in press

    Google Scholar 

  10. H. Stoof et al., Phys. Rev. Lett. 87, 120407 (2001); C. Savage, J. Ruostekoski, Phys. Rev. Lett. 91, 010403 (2003)

    Article  ADS  Google Scholar 

  11. Y.M. Cho, H. Khim, P. Zhang, Phys. Rev. A 72, 063603 (2005)

    Article  ADS  Google Scholar 

  12. E. Babaev, L. Faddeev, A. Niemi, Phys. Rev. B 65, 100512 (2002)

    Article  ADS  Google Scholar 

  13. Y.M. Cho, e-print arXiv:cond-mat/0112498; Phys. Rev. B 72, 212516 (2005)

    Article  ADS  Google Scholar 

  14. Y.M. Cho, e-print arXiv:cond-mat/0311201, Phys. Rev. B 73, 180506(R) (2006)

    Article  ADS  Google Scholar 

  15. M. Salomma, G. Volovik, Rev. Mod. Phys. 59, 533 (1987); G. Volovik, The Universe in a Helium Droplet (Clarendon Press, Oxford, 2003). See also A. Leggett, Rev. Mod. Phys. 47, 331 (1975)

    Article  ADS  Google Scholar 

  16. Y. Kondo et al., Phys. Rev. Lett. 67, 81 (1991)

    Article  ADS  Google Scholar 

  17. A. Leggett, Prog. Theo. Phys. 36, 901 (1966)

    Article  ADS  Google Scholar 

  18. Y. Izyumov, V. Laptev, Phase Transition 20, 95 (1990); M. Zhitomirsky, J. Phys. Soc. Jpn 64, 913 (1995); E, Pechenik, B. Rosenstein, B. Sapiro, I. Sapiro, Phys. Rev. B 65, 214532 (2002). See also M. Sigrist, K. Ueda, Rev. Mod. Phys. 63, 239 (1991)

    Article  Google Scholar 

  19. M. Zhitomirsky, V. Dao, Phys. Rev. B 69, 054508 (2004)

    Article  ADS  Google Scholar 

  20. E. Babaev, Phys. Rev. Lett. 89, 067001 (2002)

    Article  ADS  Google Scholar 

  21. Y. Tanaka, Phys. Rev. Lett. 88, 017002 (2002); A. Gurevich, Phys. Rev. B 67, 184515 (2003)

    Article  ADS  Google Scholar 

  22. M. Eskildsen et al., Phys. Rev. Lett. 89, 187003 (2002); A. Koshelev, A. Golubov, Phys. Rev. Lett. 90, 177002 (2003)

    Article  ADS  Google Scholar 

  23. K. Kasamatsu, M. Tsubota, M. Ueda, Phys. Rev. Lett. 93, 250406 (2004); K. Kasamatsu, M. Tsubota, M. Ueda, Phys. Rev. A 71, 043611 (2005)

    Article  ADS  Google Scholar 

  24. D. Ivanov, Phys. Rev. Lett. 86, 268 (2001); S. Chung, H. Blum, E. Kim, Phys. Rev. Lett. 99, 197002 (2007). For a review, see A. Mackenzie, Y. Maeno, Rev. Mod. Phys. 75, 657 (2003)

    Article  ADS  Google Scholar 

  25. V. Dolocan et al., Phys. Rev. Lett. 95, 097004 (2005); H. Bluhm et al., Phys. Rev. Lett. 97, 237002 (2006); A. Crisan et al., Jpn J. App. Phys. 46, 451 (2007)

    Article  ADS  Google Scholar 

  26. Y.M. Cho, Phys. Lett. B 81, 25 (1979); Y.M. Cho, Phys. Lett. B 644, 208 (2007)

    Article  ADS  Google Scholar 

  27. Y.M. Cho, Phys. Rev. D 21, 1080 (1980); Y.M. Cho, Phys. Rev. D 62, 074009 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  28. Y.M. Cho, Phys. Rev. Lett. 46, 302 (1981); Phys. Rev. D 23, 2415 (1981); W.S. Bae, Y.M. Cho, S.W. Kimm, Phys. Rev. D 65, 025005 (2002)

    Article  ADS  Google Scholar 

  29. N.D. Mermin, T.L. Ho, Phys. Rev. Lett. 36, 594 (1976)

    Article  ADS  Google Scholar 

  30. E. Simanek, Phys. Rev. B 74, 052501 (2006)

    Article  ADS  Google Scholar 

  31. K. Huang, R. Tipton, Phys. Rev. D 23, 3050 (1981)

    Article  ADS  Google Scholar 

  32. N. Ashcroft, Phys. Rev. Lett. 92, 187002 (2004); E. Babaev, A. Sudbo, N. Ashcroft, Nature 431, 666 (2004); N. Ashcroft, Phys. Rev. Lett. 95, 105301 (2005)

    Article  ADS  Google Scholar 

  33. Y.M. Cho, Phys. Lett. B 616, 101 (2005)

    Article  ADS  Google Scholar 

  34. Y.K. Bang, Y.M. Cho, Pengming Zhang, to be published

  35. P. Forgacs, S. Reuillon, M. Volkov, Phys. Rev. Lett. 96, 041601 (2006); P. Forgacs, S. Reuillon, M. Volkov, Nucl. Phys. B 751, 390 (2006)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Theoretical Physics and School of Physics, College of Natural Sciences, Seoul National University, Seoul, 151-742, Korea

    Y. M. Cho

  2. Institute of Modern Physics, Chinese Academy of Sciences, P.O. Box 31, Lanzhou, 730000, P. R. China

    P. M. Zhang

Authors
  1. Y. M. Cho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. M. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Y. M. Cho.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cho, Y.M., Zhang, P.M. Topological objects in two-gap superconductor. Eur. Phys. J. B 65, 155–178 (2008). https://doi.org/10.1140/epjb/e2008-00343-2

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2008-00343-2

PACS

Search

Navigation