Multifractally-enhanced superconductivity in thin films

TL;DR

This paper develops a theoretical framework for understanding how multifractality enhances superconductivity in thin films, revealing strong mesoscopic fluctuations and a large energy interval for the superconducting gap.

Contribution

It extends the theory of multifractal superconductivity by deriving a modified Usadel equation and analyzing spectral properties and fluctuations in thin films.

Findings

Superconducting transition temperature is enhanced by multifractality.

Disorder-averaged density of states near the spectral gap resembles a spatially random order parameter.

Strong mesoscopic fluctuations lead to a large energy interval for the superconducting gap.

Abstract

The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.