Journal of Low Temperature Physics

, Volume 171, Issue 5–6, pp 788–796 | Cite as

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

  • D. J. WeirEmail author
  • R. Monaco
  • R. J. Rivers


Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields.

Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practise, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free.


Kibble-Zurek mechanism Defect formation Superconductivity 



D.J.W. would like to thank Arttu Rajantie and Anders Tranberg for useful discussions. The simulations in this paper were performed using the Imperial College High Performance Computing Service.


  1. 1.
    T. Kibble, J. Phys. A 9, 1387 (1976) ADSzbMATHCrossRefGoogle Scholar
  2. 2.
    T. Kibble, Phys. Rep. 67, 183 (1980) MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    W. Zurek, Nature 317, 505 (1985) ADSCrossRefGoogle Scholar
  4. 4.
    W. Zurek, Acta Phys. Pol. B 24, 1301 (1993) Google Scholar
  5. 5.
    D. Golubchik, E. Polturak, G. Koren, Phys. Rev. Lett. 104, 247002 (2010) ADSCrossRefGoogle Scholar
  6. 6.
    R. Monaco, J. Mygind, M. Aaroe, R. Rivers, V. Koshelets, Phys. Rev. Lett. 96, 180604 (2006) ADSCrossRefGoogle Scholar
  7. 7.
    R. Monaco, J. Mygind, R. Rivers, V. Koshelets, Phys. Rev. B 80, 180501 (2009) ADSCrossRefGoogle Scholar
  8. 8.
    A. Yates, W. Zurek, Phys. Rev. Lett. 80, 5477 (1998) ADSCrossRefGoogle Scholar
  9. 9.
    M. Donaire, T. Kibble, A. Rajantie, New J. Phys. 9, 148 (2007) ADSCrossRefGoogle Scholar
  10. 10.
    D. Weir, R. Rivers, J. Phys. Conf. Ser. 286, 012056 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    M. Hindmarsh, A. Rajantie, Phys. Rev. Lett. 85, 4660 (2000) ADSCrossRefGoogle Scholar
  12. 12.
    A. Krasnitz, Nucl. Phys. B 455, 320 (1995) ADSCrossRefGoogle Scholar
  13. 13.
    G. Stephens, L.M. Bettencourt, W. Zurek, Phys. Rev. Lett. 88, 137004 (2002) ADSCrossRefGoogle Scholar
  14. 14.
    L. Bettencourt, G. Stephens, Phys. Rev. E 67, 066105 (2003) ADSCrossRefGoogle Scholar
  15. 15.
    K. Kajantie, M. Laine, T. Neuhaus, J. Peisa, A. Rajantie, K. Rummukainen, Nucl. Phys. B 546, 351 (1999) ADSCrossRefGoogle Scholar
  16. 16.
    D. Golubchik, E. Polturak, G. Koren, B. Shapiro, I. Shapiro, J. Low Temp. Phys. 164, 74 (2011) ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Helsinki Institute of PhysicsHelsinkiFinland
  2. 2.Istituto di Cibernetica del CNRPozzuoli (Na)Italy
  3. 3.Theoretical Physics Group, Blackett LaboratoryImperial College LondonLondonUK

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