Universal gap fluctuations in the superconductor proximity effect
M. G. Vavilov, P. W. Brouwer, V. Ambegaokar, C. W. J. Beenakker
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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