Theory of superconducting pairing near the mobility edge

TL;DR

This paper develops a theoretical framework explaining the emergence and persistence of a pseudogap in strongly disordered superconductors near the superconductor-insulator transition, highlighting the role of fractal wave functions.

Contribution

It introduces a novel theory linking fractal wave functions and attractive interactions to the pseudogap phenomenon near the SI transition.

Findings

Large pseudogap persists in the insulating state.

Analytic expressions relate pseudogap to localization properties.

Fractal wave functions significantly influence superconducting behavior.

Abstract

We develop a theory of a pseudogap state appearing near the superconductor-insulator transition in strongly disordered metals with attractive interaction. We show that such an interaction combined with the fractal nature of the single particle wave functions near the mobility edge leads to an anomalously large single particle gap in the superconducting state near SI transition that persists and even increases in the insulating state long after the superconductivity is destroyed. We give analytic expressions for the value of the pseudogap in terms of the inverse participation ratio of the corresponding localization problem.