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(theta) as a function of the angle theta between 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 and D-2, and can be very different from the one-gap dirty-limit theory. In particular, value H-c2(0) can considerably exceed 0.7T(c)dH(c2)/dT(c), which can have important consequences for applications of MgB2. Based on a general equation for H-c2(T,theta), a scaling relation, which enables one to get the angular dependence of H-c2(theta) from the equation for H-c2 at Hparallel toc, is proposed. The behavior of H-c2(theta) and H-c1(theta) can deviate markedly from the results of the anisotropic Ginzburg-Landau theory, and the ratio of the upper critical field H-c2(parallel to)/H-c2(perpendicular to) for Hparallel toab and Hperpendicular toab can both increase and decrease with temperature, depending on the relation between D-1 and D-2. Implications of the obtained results for MgB2 are discussed.