Quantum-to-classical crossover for Andreev billiards in a magnetic field

TL;DR

This paper investigates how a magnetic field influences the transition from quantum to classical behavior in Andreev billiards, revealing limitations of random-matrix theory and supporting findings with quantum simulations.

Contribution

It extends quasiclassical theory to include magnetic fields in chaotic quantum dots, highlighting the breakdown of RMT when Ehrenfest time exceeds mean reflection time.

Findings

Critical magnetic field for gap closure decreases with increased Ehrenfest time.

RMT predictions fail when Ehrenfest time surpasses mean reflection time.

Quantum simulations confirm the quasiclassical theory's predictions.

Abstract

We extend the existing quasiclassical theory for the superconducting proximity effect in a chaotic quantum dot, to include a time-reversal-symmetry breaking magnetic field. Random-matrix theory (RMT) breaks down once the Ehrenfest time $\tau_E$ becomes longer than the mean time $\tau_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $\tau_E/\tau_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).