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).

arXiv comment11 pages, 10 figures

References in corpus (25)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Random Matrix Theory of a Chaotic Andreev Quantum Dot
• Induced superconductivity distinguishes chaotic from integrable billiards
• Chaos in Andreev Billiards
• Anomalous temperature dependence of the supercurrent through a chaotic Josephson junction
• Density of States and Energy Gap in Andreev Billiards
• Dynamical model for the quantum-to-classical crossover of shot noise
• Quantum Disorder and Quantum Chaos in Andreev Billiards
• Andreev billiards
• Superconductor-proximity effect in chaotic and integrable billiards
• Quantum Andreev map: A paradigm of quantum chaos in superconductivity
• Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field
• Noiseless scattering states in a chaotic cavity
• Quantum interference and the formation of the proximity effect in chaotic normal-metal/superconducting structures
• Adiabatic quantization of Andreev levels
• Quantum-to-classical crossover of mesoscopic conductance fluctuations
• Microscopic Theory for the Quantum to Classical Crossover in Chaotic Transport
• Efficient Diagonalization of Kicked Quantum Systems
• Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard
• Exponential sensitivity to dephasing of electrical conduction through a quantum dot
• Weak localization of the open kicked rotator
• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quasiclassical fluctuations of the superconductor proximity gap in a chaotic system
• A pseudointegrable Andreev billiard

Cited by in corpus (13)

• Semiclassical Theory of Quantum Chaotic Transport: Phase-Space Splitting, Coherent Backscattering and Weak Localization
• A semiclassical theory of the Ehrenfest-time dependence of quantum transport in ballistic quantum dots
• 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
• Ehrenfest-time dependence of counting statistics for chaotic ballistic systems
• The density of states of chaotic Andreev billiards
• Superconductivity-induced macroscopic resonant tunneling
• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Spectrum of the Andreev Billiard and Giant Fluctuations of the Ehrenfest Time
• Non-retracing orbits in Andreev billiards
• Effect of spin-orbit coupling on the excitation spectrum of Andreev billiards
• Macroscopic Resonant Tunneling through Andreev Interferometers
• Quantized invariant tori in Andreev billiards of mixed phase space