Enhancement of the upper critical field by nonmagnetic impurities in dirty two-gap superconductors

Quasiclassic Usadel equations for two-band superconductors in the dirty limit are derived with the account of both intraband and interband scattering by nonmagnetic impurities. From these equations, the Ginzburg-Landau equations, and the equations for the critical temperature ${T}_{c}$ and the upper critical field ${H}_{c2}$ are obtained. The equation for ${H}_{c2}$ determines both the temperature dependence of ${H}_{c2}(T)$ and the orientational dependence of ${H}_{c2}(\ensuremath{\theta})$ as a function of the angle $\ensuremath{\theta}$ between $\mathbf{H}$ and the c axis. It is shown that the shape of the ${H}_{c2}(T)$ curve essentially depends on the ratio of the intraband electron diffusivities ${D}_{1}$…