Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system

TL;DR

This paper investigates the fluctuations of the superconducting proximity gap in chaotic systems, revealing a transition from quantum to quasiclassical behavior depending on the Ehrenfest time, with implications for understanding mesoscopic superconductivity.

Contribution

It demonstrates how the magnitude of gap fluctuations depends on the Ehrenfest time, bridging quantum and classical descriptions in chaotic superconducting systems.

Findings

Quantum fluctuations match random-matrix theory predictions for small Ehrenfest times.

Fluctuations become much larger than level spacing for larger Ehrenfest times.

Gap fluctuations are correlated with classical dwell-time distributions in the quasiclassical regime.

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 $\tau_E\ll\hbar/E_T$ (with $\tau_E$ the Ehrenfest time and $E_T$ the Thouless energy). For $\tau_E\agt\hbar/ E_T$ 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.