Multifractally-enhanced superconductivity in thin films

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.

30 pages, 3 figures, accepted to Localisation 2020 volume of Annals of Physics

References in corpus (6)

• Anderson Transitions
• Localization of preformed Cooper-pairs in disordered superconductors
• Disorder-Induced Inhomogeneities of the Superconducting State Close to the Superconductor-Insulator Transition
• Eigenfunction fractality and pseudogap state near superconductor-insulator transition
• Quantum breakdown of superconductivity in low-dimensional materials
• Keldysh Ginzburg-Landau action of fluctuating superconductors

Cited by in corpus (18)

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• Multifractally-enhanced superconductivity in two-dimensional systems with spin-orbit coupling
• Interplay of superconductivity and localization near a 2D ferromagnetic quantum critical point
• Generalized multifractality in the spin quantum Hall symmetry class with interaction
• Generalized surface multifractality in 2D disordered systems
• Local density of state fluctuations in 2D superconductor as a probe of quantum diffusion
• Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid
• Boundary multifractality in the spin quantum Hall symmetry class with interaction
• Quantum Fluctuations and Multifractally-Enhanced Superconductivity in Disordered Thin Films
• Exploring the vortex phase diagram of Bogoliubov-de Gennes disordered superconductors
• Superconducting Diode Effect in Weak Localization Regime
• Multifractal correlations of the local density of states in dirty superconducting films
• Superfluid transition in quasi-two-dimensional disordered dipolar Fermi gases