Usadel's dirty-limit version of the Gorkov-Eilenberger theory including strong-coupling effects is used to calculate the lower critical field of superconducting alloys. The results of the (rigorous) numerical study, which is valid for all temperatures and Ginzburg-Landau parameters κ, are compared with experiments and with the existing weak-coupling theory. One achieves agreement with the bulk of the experimental results only if κ is properly adjusted. In addition, it is shown that a circular-cell approximation for the vortex state yields highly accurate magnetization curves, which are influenced in a characteristic way by strong electron-phonon coupling.
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Rammer, J. Lower critical field and magnetization of strong-coupling, type II superconductors in the dirty limit. J Low Temp Phys 71, 323–340 (1988). https://doi.org/10.1007/BF00116866
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DOI: https://doi.org/10.1007/BF00116866