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

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).

11 pages, 10 figures

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• Andreev billiards
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Cited by in corpus (7)

• Quantum-to-classical correspondence in open chaotic systems
• Towards a semiclassical justification of the `effective random matrix theory' for transport through ballistic chaotic quantum dots
• Superconductivity-induced macroscopic resonant tunneling
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Quantized invariant tori in Andreev billiards of mixed phase space