Ballistic and diffusive: theory of vortices in the two-band   superconductor MgB2
  Motivated by the recent results on impurity effects in MgB2, we present a theoretical model for a two-band superconductor in which the character of quasiparticle motion is ballistic in one band and diffusive in the other. We apply our model to calculate the electronic structure in the vicinity of an isolated vortex. We assume that superconductivity in the diffusive (pi) band is induced by that in the clean (sigma) band, as suggested by experimental evidence for MgB2. We focus our attention to the spatial variations of the order parameter, the current density, and the vortex core spectrum in the two bands. Our results indicate that the coupling to the pi band can lead to the appearance of additional bound states near the gap edge in the sigma band that are absent in the single-band case. 
K. Tanaka, D.F. Agterberg, J. Kopu, M. Eschrig