Superconductor-proximity effect in chaotic and integrable billiards

Abstract

We explore the effects of the proximity to a superconductor on the level density of a billiard for the two extreme cases that the classical motion in the billiard is chaotic or integrable. In zero magnetic field and for a uniform phase in the superconductor, a chaotic billiard has an excitation gap equal to the Thouless energy. In contrast, an integrable (rectangular or circular) billiard has a reduced density of states near the Fermi level, but no gap. We present numerical calculations for both cases in support of our analytical results. For the chaotic case, we calculate how the gap closes as a function of magnetic field or phase difference.

4 pages, RevTeX, 2 Encapsulated Postscript figures. To be published by Physica Scripta in the proceedings of the "17th Nordic Semiconductor Meeting", held in Trondheim, June 1996

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• Induced superconductivity distinguishes chaotic from integrable billiards
• Correlation Functions in Disordered Systems
• Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field
• Magnetoconductance of ballistic chaotic quantum dots: A Brownian motion approach for the $S$-matrix

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