Eigenfunction fractality and pseudogap state near superconductor-insulator transition

TL;DR

This paper develops a theory explaining the emergence of a pseudogap state near the superconductor-insulator transition in disordered metals, linking fractal wave functions and attractive interactions to a persistent, large single-particle gap.

Contribution

It introduces a novel theoretical framework connecting fractal wave functions and pseudogap formation near the superconductor-insulator transition.

Findings

Large pseudogap persists in the insulating state

Analytic expressions relate pseudogap to inverse participation ratio

Fractal nature of wave functions influences superconducting properties

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.