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The multifractal superconducting state originates from the interplay ofAnderson localization and interaction effects. In this article we overview therecent theory of the superconductivity enhancement by multifractality andextend it to describe the spectral properties of superconductors on the scalesof the order of the superconducting gap. Specifically, using the approach basedon renormalization group within the nonlinear sigma model, we develop thetheory of a multifractal superconducting state in thin films. We derive amodified Usadel equation that incorporates the interplay of disorder andinteractions at energy scales larger than the spectral gap and study the effectof such an interplay on the low-energy physics. We determine the spectral gapat zero temperature which occurs to be proportional to the multifracallyenhanced superconducting transition temperature. The modified Usadel equationresults in the disorder-averaged density of states that, near the spectral gap,resembles the one obtained in the model of a spatially random superconductingorder parameter. We reveal strong mesoscopic fluctuations of the local densityof states in the superconducting state. Such strong mesoscopic fluctuationsimply that the interval of energies in which the superconducting gapestablishes is parametrically large in systems with multifractally-enhancedsuperconductivity.

Multifractally-enhanced superconductivity in thin films