Semiclassical theory of quasiparticles in giant vortices

Abstract

Methods for investigating Andreev bound states in superconducting vortices continue to be of experimental and theoretical interest [Phys. Rev. Lett. 90 (2003) 177002]. We have recently developed a semiclassical theory of quasiparticles in the superconducting state [Ann. Phy. (NY) 298 (2002) 273]. It is based upon the study of classical orbits, the Bogoliubov–de Gennes equation being replaced by Hamiltonian systems describing an effective (fictious) classical mechanics. The orbits are quantised using a generalisation of the Bohr–Sommerfeld or EBK quantisation rule which includes both a Maslov index and an additional topological integer arising from the lines of phase singularity running along the vortex cores. We deploy this theory to the spectra of a single giant vortex.