Vortex core shrinkage in a two gap superconductor: application to MgB2
  As a model for the vortex core in MgB2 we study a two band model with a clean sigma band and a dirty pi band. We present calculations of the vortex core size in both bands as a function of temperature and show that there exists a Kramer-Pesch effect in both bands even though only one of the bands is in the clean limit. We present calculations for different pi band diffusivities and coherence lengths. 
S. Graser, A. Gumann, T. Dahm, and N. Schopohl