Journal of Low Temperature Physics

, Volume 188, Issue 1–2, pp 39–48 | Cite as

Finite Element Treatment of Vortex States in 3D Cubic Superconductors in a Tilted Magnetic Field

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Abstract

The time-dependent Ginzburg–Landau equations have been solved numerically by a finite element analysis for superconducting samples with a cubic shape in a tilted magnetic field. We obtain different vortex patterns as a function of the external magnetic field. With a magnetic field not parallel to the x- or y-axis, the vortices attempt to change their orientation accordingly. Our analysis of the corresponding changes in the magnetic response in different directions can provide information not only about vorticity but also about the three-dimensional vortex arrangement, even about the very subtle changes for the superconducting samples with a cubic shape in a tilted magnetic field.

Keywords

Three-dimensional cubic superconductors TDGL equations Finite element method Vortex states 

Notes

Acknowledgements

This work is sponsored by the Science and Technology Commission of Shanghai Municipality (14521102800), the National Natural Science Foundation of China (51202141), the Opening Project of Shanghai Key Laboratory of High Temperature Superconductors (14DZ2260700), the Natural Science Foundation of Shanghai (No.17ZR1411400), the Shanghai plateau project (Shanghai University of Electric Power) and the Innovation Program of Shanghai Municipal Education Commission (No. 14YZ132).

References

  1. 1.
    R. Geurts, M.V. Milošević, F.M. Peeters, Phys. Rev. B 75, 184511 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    I.V. Grigorieva, W. Escoffier, J. Richrdson, L.Y. Vinnikov, S. Dubonos, V. Oboznov, Phys. Rev. Lett. 96, 077005 (2006)ADSCrossRefGoogle Scholar
  3. 3.
    G.R. Berdiyorov, M.V. Milošević, M.L. Latimer, Z.L. Xiao, W.K. Kwok, F.M. Peeters, Phys. Rev. Lett. 109, 057004 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    Xu Ben, M.V. Milošević, F.M. Peeters, Phys. Rev. B 81, 064501 (2010)Google Scholar
  5. 5.
    T. Cren, L. Serrier-Garcia, F. Debontridder, D. Roditchev, Phys. Rev. Lett. 107, 097202 (2011)ADSCrossRefGoogle Scholar
  6. 6.
    A. Kanda, B.J. Baelus, F.M. Peeters, K. Kadowaki, Y. Ootuka, Phys. Rev. Lett. 93, 257002 (2004)ADSCrossRefGoogle Scholar
  7. 7.
    M.V. Milošević, A. Kanda, S. Hatsumi, F.M. Peeters, Y. Ootuka, Phys. Rev. Lett. 103, 217003 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    T. Winiecki, C.S. Adams, J. Comput. Phys. 179, 127 (2002)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Ž.L. Jelić, M.V. Milošević, J. de Van Vondel, A.V. Silhanek, Sci. Rep. 5, 14604 (2015). doi:10.1038/srep14604 ADSCrossRefGoogle Scholar
  10. 10.
    L. Peng, C. Cai, J. Lin, J. Chen, Y. Liu, Y. Zhou, J. Supercond. Nov. Magn. 29, 1197 (2016)CrossRefGoogle Scholar
  11. 11.
    B.J. Baelus, F.M. Peeters, Phys. Rev. B 65, 104515 (2002)ADSCrossRefGoogle Scholar
  12. 12.
    L. Peng, C. Cai, J. Low Temp. Phys. 183, 371 (2016)ADSCrossRefGoogle Scholar
  13. 13.
    W.H. Kleiner, L.M. Roth, S.H. Autler, Phys. Rev. 133, A1226 (1964)ADSCrossRefGoogle Scholar
  14. 14.
    L.F. Chibotaru, A. Ceulemans, V. Bruyndoncx, V.V. Moshchalkov, Nat. (Lond.) 408, 833 (2000)ADSCrossRefGoogle Scholar
  15. 15.
    W.A. Little, R.D. Parks, Phys. Rev. Lett. 9, 9 (1962)ADSCrossRefGoogle Scholar
  16. 16.
    C. Carballeira, V.V. Moshchalkov, L.F. Chibotaru, A. Ceulemans, Phys. Rev. Lett. 95, 237003 (2005)ADSCrossRefGoogle Scholar
  17. 17.
    M.V. Milošević, F.M. Peeters, Phys. Rev. Lett. 94, 227001 (2005)ADSCrossRefGoogle Scholar
  18. 18.
    Chao-Yu. Liu, G.R. Berdiyorov, M.V. Milošević, Phys. Rev. B 83, 104524 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    G. Deutscher, P.G. de Gennes, in Superconductivity, ed. by R.D. Parks vol. 2, Chap. 17 (Marcel Dekker, New York, 1969)Google Scholar
  20. 20.
    L. Peng, Y. Liu, C. Chen, H. Li, C. Jia, Q. Zou, J. Low Temp. Phys. 170, 91 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    E. Šimánek, Phys. Rev. B 65, 184524 (2002)CrossRefGoogle Scholar
  22. 22.
    R. Zadorosny, E. Sardella, A.L. Malvezzi, P.N. Lisboa-Filho, W.A. Ortiz, Phys. Rev. B 85, 214511 (2012)ADSCrossRefGoogle Scholar
  23. 23.
    T.S. Alstrøm, M.P. Sørensen, N.F. Pedersen, S. Madsen, Acta. Appl. Math. 115, 63 (2011)MathSciNetCrossRefGoogle Scholar
  24. 24.
    V.M. Kranov, V.A. Oboznov, V.V. Ryazanov, N. Mros, A. Yurgens, Winkler, Phys. Rev. B 61, 766 (2000)ADSCrossRefGoogle Scholar
  25. 25.
    J.F. Blackburn, A. Campbell, E.K.H. Salje, Philos. Mag. B 80, 1455 (2000)ADSCrossRefGoogle Scholar
  26. 26.
    V.M. Fomin, J.T. Devreese, V.V. Moshchalkov, Europhys. Lett. 42, 553 (1998)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of PhysicsShanghai University of Electric PowerShanghaiChina
  2. 2.Shanghai Key Laboratory of High Temperature Superconductors, Physics DepartmentShanghai UniversityShanghaiChina

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