Mixed state in dirty two-band superconductors: appliation to MgB2

We investigate a two-band superconductor with strong intraband and weak interband electronic scattering rates in the framework of coupled Usadel equations. We calculate the upper critical field for different field orientation. Due to a very large difference between the c-axis coherence lengths in two-bands, the GL theory is applicable only in the extremely narrow temperature range. This leads to the strong temperature dependence of the Hc2 anisotropy and large deviations of the angular dependence of Hc2 from a simple effective-mass law. In the case of field along c-direction we solved coupled nonlinear Usadel equations numerically to find field evolution of the pair potentials and local densities of states for two-bands. The existence of two distinct length and field scales corresponding to different bands is demonstrated.