Non-retracing orbits in Andreev billiards

Abstract

The validity of the retracing approximation in the semiclassical quantization of Andreev billiards is investigated. The exact energy spectrum and the eigenstates of normal-conducting, ballistic quantum dots in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes equation and compared with the semiclassical Bohr-Sommerfeld quantization for periodic orbits which result from Andreev reflections. We find deviations that are due to the assumption of exact retracing electron-hole orbits rather than the semiclassical approximation, as a concurrently performed Einstein-Brillouin-Keller quantization demonstrates. We identify three different mechanisms producing non-retracing orbits which are directly identified through differences between electron and hole wave functions.

9 pages, 12 figures, Phys. Rev. B (in print), high resolution images available upon request

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Cited by in corpus (4)

• Quantum-classical correspondence in the wavefunctions of Andreev billiards
• Decreasing excitation gap in Andreev billiards by disorder scattering
• Scanning gate microscopy of nonretracing electron-hole trajectories in a normal-superconductor junction
• Quantized invariant tori in Andreev billiards of mixed phase space