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

Goorden, M. C.; Jacquod, Ph.; Beenakker, C. W. J.

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

Authors

Goorden, M. C.

Jacquod, Ph.

Beenakker, C. W. J.

Description

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 $τ_E$ becomes longer than the mean time $τ_D$ between Andreev reflections. As a consequence, the critical field at which the excitation gap closes drops below the RMT prediction as $τ_E/τ_D$ is increased. Our quasiclassical results are supported by comparison with a fully quantum mechanical simulation of a stroboscopic model (the Andreev kicked rotator).
11 pages, 10 figures