Semiclassical theory of quasiparticles in the superconducting state

Abstract

We have developed a semiclassical approach to solving the Bogoliubov - de Gennes equations for superconductors. It is based on the study of classical orbits governed by an effective Hamiltonian corresponding to the quasiparticles in the superconducting state and includes an account of the Bohr-Sommerfeld quantisation rule, the Maslov index, torus quantisation, topological phases arising from lines of phase singularities (vortices), and semiclassical wave functions for multi-dimensional systems. The method is illustrated by studying the problem of an SNS junction and a single vortex.