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Mikhail Feigel’man - Landau Institute for Theoretical Physics

Fractal superconductivity near localization threshold


We develop a semi-quantitative theory of electron pairing correlations in bulk "poor conductors" with a weak attractive Cooper interaction, at Fermi energies near the Anderson mobility edge. Fractal nature of critical wavefunction’s correlations is shown to be crucial for the physics discussed. We analyzed three distinct phases of such a system : i) "critical" superconductive state formed, ii) superconductive state with a strong pseudogap, realized due to pairing of weakly localized electrons (with relatively large single-particle localization length), and iii) insulating state realized deeper inside localized band. For the state i) our main findings are as follows : at weak coupling, transition temperature can be enhanced considerably with respect to BCS result ; spatial distribution of superconductive order parameter is extremely inhomogeneous, in spite of a well-defined transition temperature ; the same is true for local density of states and tunneling conductance which acquires strong random asymmetry with respect to the sign of voltage. The major new feature of the pseudo¬gaped state is the presence of two independent energy scales : in addition to superconductive gap ∆, that is due to many-body correlations, a new "pseudogap" energy scale ∆P comes into play ; the latter characterizes typical binding energy of localized electron pairs and leads to insulating trend of the resistivity-vs-temperature behavior above superconductive Tc. Two¬gap nature of the "pseudo-gaped superconductor" is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We also show that pseudo-gaped superconductive state should demonstrate strong non-conservation of full spectral weight of high-frequency conductivity. Finally, the state iii) is realized due to presence of local binding gap but without superconducting correlations ; it is shown to possess (almost) hard insulating gap and thus purely activated low-temperature resistivity lnR(T) T-1. A new "pseudospin" scenario of superconductor-insulator transition is proposed, based on the above results.

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