Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system

Abstract

We calculate the sample-to-sample fluctuations in the excitation gap of a chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum fluctuations on the order of magnitude of the level spacing, predicted by random-matrix theory, apply if ${\tau }_E\ll \hslash /E_T$ (with ${\tau }_E$ the Ehrenfest time and $E_T$ the Thouless energy). For $τ_E\agt\hbar/ E_T$ the fluctuations are much greater than the level spacing. We demonstrate the quasiclassical nature of the gap fluctuations in the large-${\tau }_E$ regime by correlating them to an integral over the classical dwell-time distribution.

arXiv comment4 pages, 3 figures

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• Effective Random Matrix Theory description of chaotic Andreev billiards
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Microscopic theory of the Andreev gap
• Low-energy quasiparticle excitations in dirty d-wave superconductors and the Bogoliubov-de Gennes kicked rotator
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Breakdown of Universality in Quantum Chaotic Transport: the Two-Phase Dynamical Fluid Model