Universal gap fluctuations in the superconductor proximity effect

Abstract

Random-matrix theory is used to study the mesoscopic fluctuations of the excitation gap in a metal grain or quantum dot induced by the proximity to a superconductor. We propose that the probability distribution of the gap is a universal function in rescaled units. Our analytical prediction for the gap distribution agrees well with exact diagonalization of a model Hamiltonian.

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• Quantum Disorder and Quantum Chaos in Andreev Billiards
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• Large deviations of the top eigenvalue of large Cauchy random matrices
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• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
• Subgap states in disordered superconductors with strong magnetic impurities
• Density of States in a Mesoscopic SNS Junction
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• Superconductor-proximity effect in hybrid structures: Fractality versus Chaos
• Delay-Time and Thermopower Distributions at the Spectrum Edges of a Chaotic Scatterer
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• Tail States below the Thouless Gap in SNS junctions: Classical Fluctuations
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• Mesoscopic fluctuations in superconductor-topological insulator Josephson junctions
• Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states