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 with 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 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 of the momentum within a band. In the framework of this model all thermodynamic variables can be found explicitly at any value of the scattering rate. This solution explains the sample dependence of the specific-heat discontinuity in MgB₂ and the influence of disorder on the critical temperature.