Scattering of Single-Particle Excitations by a Vortex in a Clean Type-II Superconductor

Abstract

A study of the scattering of BCS single-particle excitations by an isolated vortex in a clean type-II superconductor is reported. The coupled Bogoliubov equations provide a theoretical framework for calculating quasiparticle wave functions. The vortex introduces superfluid velocity into the metal, depresses the order parameter $\ensuremath{\Delta}(r)$ at the core, and gives rise to a Bohm-Aharonov effect. The scattering problem has two channels with coupling between particlelike and holelike excitations. The total cross section diverges because of the Bohm-Aharonov effect, but the cross section ${\ensuremath{\sigma}}_{s}$ for a particle to scatter from one channel to the other remains finite. This quantity ${\ensuremath{\sigma}}_{s}$ is also equal to one-half the transport cross section. A numerical evaluation of ${\ensuremath{\sigma}}_{s}$ as a function of the energy and polar angle of the excitations relative to the external field has been made.