title: Semiclassical Quantization of Spinning Quasiparticles in Ballistic Josephson Junctions.
abstract: A Josephson junction made of a generic magnetic material sandwiched between two conventional superconductors is studied in the ballistic semiclassic limit. The spectrum of Andreev bound states is obtained from the single valuedness of a particle-hole spinor over closed orbits generated by electron-hole reflections at the interfaces between superconducting and normal materials. The semiclassical quantization condition is shown to depend only on the angle mismatch between initial and final spin directions along such closed trajectories. For the demonstration, an Andreev-Wilson loop in the composite position-particle-hole-spin space is constructed and shown to depend on only two parameters, namely, a magnetic phase shift and a local precession axis for the spin. The details of the Andreev-Wilson loop can be extracted via measuring the spin-resolved density of states. A Josephson junction can thus be viewed as an analog computer of closed-path-ordered exponentials.
authors.affiliation: Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 5, E-20018 San Sebastián, Spain.
authors.forename: François
authors.initials: F
authors.lastname: Konschelle
authors.affiliation: Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, Manuel de Lardizabal 5, E-20018 San Sebastián, Spain.|Donostia International Physics Center (DIPC), Manuel de Lardizabal 4, E-20018 San Sebastián, Spain.
authors.forename: F Sebastián
authors.initials: FS
authors.lastname: Bergeret
authors.affiliation: Nano-Bio Spectroscopy group, Departamento Física de Materiales, Universidad del País Vasco, Avenida Tolosa 72, E-20018 San Sebastián, Spain.|IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain.
authors.forename: Ilya V
authors.initials: IV
authors.lastname: Tokatly