Localization of quasiparticles in a disordered vortex

We study the diffusive motion of low-energy normal quasiparticles along the core of a single vortex in a dirty, type-II, s-wave superconductor. The physics of this system is argued to be described by a one-dimensional supersymmetric non-linear a model, which differs from the a models known for disordered metallic wires. For an isolated vortex and quasiparticle energies less than the Thouless energy E-Th, We recover the spectral correlations that are predicted by random matrix theory for the universality class C, We then consider the transport problem of transmission of quasiparticles through a vortex connected to particle reservoirs at both ends. The transmittance at zero energy exhibits a weak localization correction reminiscent of quasi-one-dimensional metallic systems with symmetry index beta = 1. Weak localization disappears with increasing energy over a scale set by E-Th. This crossover should be observable in measurements of the longitudinal he:at conductivity of an ensemble of vortices under mesoscopic conditions. In the regime of strong localization, the localization length is shown to decrease by a factor of 8 as the quasiparticle energy goes to zero, (C) 1998 Elsevier Science B.V.