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On non‐local extensions of the ginsburg‐landau theory for type‐II superconductors valid at all temperatures
Author(s) -
Brandt E. H.
Publication year - 1973
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220570127
Subject(s) - superconductivity , condensed matter physics , physics , magnetization , energy functional , invariant (physics) , lattice (music) , mathematical physics , ginzburg–landau theory , series (stratigraphy) , magnetic field , mathematics , quantum mechanics , paleontology , acoustics , biology
The free energy of a superconductor is expressed as a two‐dimensional infinite series which may be interpreted in three different ways: as an expansion with respect to a) the gap parameter, b) the gauge‐invariant gradient, or c) the temperature difference T c ‐ T. By partial summation of the series we obtain a simple non‐local functional containing as special cases the extended Ginsburg‐Landau theory (Neumann‐Tewordt) and the nonlocal electrodynamics (Pippard, Gorkov). For small magnetization it gives the exact gap (Helfand‐Werthamer) and the magnetic field distribution (Delrieu) in the entire temperature range 0≦ T < T c In the general case the functional is expected to be a good approximation for T > 0.7 T c By numerical minimization of the functional one may hope to solve fairly complicated problems such as, e.g., the perturbed flux‐line lattice.