Quantum-classical correspondence in the wavefunctions of Andreev billiards

Abstract

We present a classical and quantum mechanical study of an Andreev billiard with a chaotic normal dot. We demonstrate that in general the classical dynamics of these normal-superconductor hybrid systems is mixed, thereby indicating the limitations of a widely used retracing approximation. We show that the mixed classical dynamics gives rise to a wealth of wavefunction phenomena, including periodic orbit scarring and localization of the wavefunction onto other classical phase space objects such as intermittent regions and quantized tori.

4 pages, 4 figures, good quality figures are available upon request

References in corpus (8)

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• Adiabatic quantization of Andreev levels
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• Effective Random Matrix Theory description of chaotic Andreev billiards
• Quantum-to-classical crossover for Andreev billiards in a magnetic field
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Cited by in corpus (5)

• Goos-Haenchen shift and localization of optical modes in deformed microcavities
• Non local Andreev reflection in a carbon nanotube superconducting quantum interference device
• Scanning gate microscopy of nonretracing electron-hole trajectories in a normal-superconductor junction
• Non-universal suppression of the excitation gap in chaotic Andreev billiards: Superconducting terminals as sensitive probes for scarred states
• Quantized invariant tori in Andreev billiards of mixed phase space