2005/04/05 by Florian Libisch, F. Libisch, S. Rotter +7 · 1 citation
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Physics of Superconductivity and Magnetism #Quantum chaos and dynamical systems #cond-mat.mes-hall
paper · pdf · doi:10.1103/physrevb.72.075304
published as Phys. Rev. B 72, 075304 (2005). · 8 pages, 6 figures, submitted to Phys. Rev
arxiv created 2005/04/05 · openalex publication_date 2005/08/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The energy spectrum and the eigenstates of a rectangular quantum dot containing soft potential walls in contact with a superconductor are calculated by solving the Bogoliubov--de Gennes equation. We compare the quantum mechanical solutions with a semiclassical analysis using a Bohr-Sommerfeld (BS) quantization of periodic orbits. We propose a simple extension of the BS approximation which is well suited to describe Andreev billiards with parabolic potential walls. The underlying classical periodic electron-hole orbits are directly identified in terms of ``scar''-like features engraved in the quantum wave functions of Andreev states which we determine here explicitly.