Specific Heat Discontinuity in Impure Two-Band Superconductors
  The Ginzburg-Landau coefficients, and the jump of the specific heat are calculated for a disordered two-band superconductor. We start with the analysis of a more general case arbitrary anisotropy. While the specific heat discontinuity at the critical temperature T_c decreases with increasing disorder, its ratio to the normal state specific heat at T_c increases and slowly converges to the isotropic value. For a strong disorder the deviation from the isotropic value is proportional to the elastic electron scattering time. In the case of a two-band superconductor we apply a simplified model of the interaction independent on momentum within a band. In the framework of this model all thermodynamic values can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific heat discontinuity in MgB_2 and the influence of the disorder on the critical temperature. 
Todor M. Mishonov, Evgeni S. Penev, Joseph O. Indekeu, and Valery L.   Pokrovsky