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Non-retracing orbits in Andreev billiards

F. Libisch·S. Rotter·J. Burgdoerfer
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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.

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F. Libisch, S. Rotter, J. Burgdoerfer. 2005-12-13. Non-retracing orbits in Andreev billiards. https://doi.org/10.1103/physrevb.73.045324

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