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Abstract: We develop a semi-quantitative theory of electron pairing and resultingsuperconductivity in bulk -poor conductors- in which Fermi energy $E F$ islocated in the region of localized states not so far from the Anderson mobilityedge $E c$. We review the existing theories and experimental data and arguethat a large class of disordered films is described by this model.Our theoretical analysis is based on the analytical treatment of pairingcorrelations, described in the basis of the exact single-particle eigenstatesof the 3D Anderson model, which we combine with numerical data on eigenfunctioncorrelations. Fractal nature of critical wavefunction-s correlations is shownto be crucial for the physics of these systems.We identify three distinct phases: -critical- superconductive state formed at$E F=E c$, superconducting state with a strong pseudogap, realized due topairing of weakly localized electrons and insulating state realized at $E F$still deeper inside localized band. The -critical- superconducting phase ischaracterized by the enhancement of the transition temperature with respect toBCS result, by the inhomogeneous spatial distribution of superconductive orderparameter and local density of states. The major new feature of thepseudo-gaped state is the presence of two independent energy scales:superconducting gap $\Delta$, that is due to many-body correlations and a new-pseudogap- energy scale $\Delta P$ which characterizes typical binding energyof localized electron pairs and leads to the insulating behavior of theresistivity as a function of temperature above superconductive $T c$. Two gapnature of the -pseudo-gaped superconductor- is shown to lead to a number ofunusual physical properties.

Author: M. V. Feigel'man, L. B. Ioffe, V. E. Kravtsov, E. Cuevas


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