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Dual Description of the Superconducting Phase Transition
Author(s) -
Kiometzis Michael,
Kleinert Hagen,
Schakel Adriaan M. J.
Publication year - 1995
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190430803
Subject(s) - condensed matter physics , physics , superconductivity , magnetic field , phase transition , critical exponent , vortex , ginzburg–landau theory , superfluidity , cooper pair , landau theory , meissner effect , scalar (mathematics) , quantum mechanics , mathematics , geometry , thermodynamics
Abstract The dual approach to the Ginzburg‐Landau theory of a Bardeen‐Cooper‐Schrieffer superconductor is reviewed. The dual theory describes a grand canonical ensemble of fluctuating closed magnetic vortices, of arbitrary length and shape, which interact with a massive vector field representing the local magnetic induction. When the critical temperature is approached from below, the magnetic vortices proliferate. This is signaled by the disorder field, which describes the loop gas, developing a non‐zero expectation value in the normal conducting phase. It therby breaks a global U(1) symmetry. The ensuing Goldstone field is the magnetic scalar potential. The superconducting‐to‐normal phase transition is studied by applying renormalization group theory to the dual formulation. In the regime of a second‐order transition, the critical exponents are given by those of a superfluid with a reversed temperature axis.