SKM 2021 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 1: Focus Session: Disordered and Granular Superconductors: Fundamentals and Applications in Quantum Technology I
TT 1.4: Vortrag
Montag, 27. September 2021, 11:00–11:15, H6
Distribution of the order parameter in strongly disordered superconductors: analytic theory — •Anton V. Khvalyuk1,2 and Mikhail V. Feigel’man2,3 — 1Skolkovo Institute of Science and Technology, 143026 Skolkovo, Russia — 2L. D. Landau Institute for Theoretical Physics, 119334 Moscow, Russia — 3Moscow Institute of Physics and Technology, 117303 Dolgoprudny, Russia
We present an analytic theory of inhomogeneous superconducting pairing in strongly disordered materials, which are moderately close to Superconducting-Insulator Transition. Within our model, single-electron eigenstates are assumed to be Anderson-localized, with a large localization volume. Superconductivity then develops due to coherent delocalization of originally localized preformed Cooper pairs. The key assumption of the theory is that each such pair is coupled to a large number Z≫1 of similar neighboring pairs. We derived integral equations for the probability distribution P(Δ) of local superconducting order parameter Δ(r) and analyzed their solutions in the limit of small dimensionless Cooper coupling constant λ≪1. The shape of the order-parameter distribution is found to depend crucially upon the effective number of "nearest neighbors" Zeff=2ν0Δ Z. The solution we provide is valid both at large and small Zeff; the latter case is nontrivial as the function P(Δ) is heavily non-Gaussian. One of our key findings is the discovery of a broad range of parameters where the distribution function P(Δ) is non-Gaussian but also free of "fat tails" and other features of criticality. The analytic results are supplemented by numerical data, and good agreement between them is observed.