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

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

2005-05-09

arxiv.org/abs/cond-mat/0505206v2

Phys. Rev. B 72, 064526 (2005)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

11 pages, 10 figures

Scientific paper

10.1103/PhysRevB.72.064526

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).

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