Mean-field theory of strongly disordered superconductors

Details Mean-field theory of strongly disordered superconductors Mean-field theory of strongly disordered superconductors

1999-02-22

arxiv.org/abs/cond-mat/9902305v2

Int. J. Mod. Phys. B, vol. 14, p. 575 (2000)

Physics

Condensed Matter

Superconductivity

15 pages, LaTex, 3 Postscript figures, additional explanations, references added, typos corrected

Scientific paper

10.1142/S0217979200000522

Qualitative features of the mean-field theory of superconductivity in a strongly disordered systems of fermions with short-range attraction are discussed. In this limit the effective theory is entirely bosonic, and I consider both the artificial infinite-range limit, and the more realistic case of "nearest neighbor" hopping of bosons between localized states. In the infinite range case the mean-field theory is exact, and the superconducting gap is uniform in space. There is a smooth BCS-BEC crossover with decrease in density, at weak enough disorder; at moderate densities, or larger disorder, the mean-field ground state is the BCS-like localized superconductor. In the latter case, the gap is highly non-uniform in space, but surprisingly stays everywhere finite below the mean-field transition temperature.

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