Frontiers of Physics

, Volume 6, Issue 4, pp 357–369 | Cite as

Electrodynamics of Abrikosov vortices: the field theoretical formulation

  • Aron J. Beekman
  • Jan Zaanen
Research Article


Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding principles.We demonstrate that the relativistic vortex worldsheet in spacetime is the object that naturally conveys all electric and magnetic information, for which we obtain simple and concise equations. Breaking Lorentz invariance leads to down-to-earth Abrikosov vortices, and special limits of these equations include for instance dynamic Meissner screening and the AC Josephson relation. On a deeper level, we explore the electrodynamics of two-form sources in the absence of electric monopoles, in which the electromagnetic field strength itself acquires the characteristics of a gauge field. This novel framework leaves room for unexpected surprises.


Abrikosov vortex electromagnetism Maxwell equations differential geometry multivalued fields 


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© Higher Education Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Instituut-Lorentz for Theoretical PhysicsUniversiteit LeidenLeidenThe Netherlands

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