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

Abstract

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 Tc and the upper critical field Hc2 are obtained. The equation for Hc2 determines both the temperature dependence of Hc2(T) and the orientational dependence of Hc2(θ) as a function of the angle θ between H and the c axis. It is shown that the shape of the Hc2(T) curve essentially depends on the ratio of the intraband electron diffusivities D1 and D2, and can be very different from the one-gap dirty-limit theory. In particular, value Hc2(0) can considerably exceed 0.7TcdHc2/dTc, which can have important consequences for applications of MgB2. Based on a general equation for Hc2(T,θ), a scaling relation, which enables one to get the angular dependence of Hc2(θ) from the equation for Hc2 at H‖c, is proposed. The behavior of Hc2(θ) and Hc1(θ) can deviate markedly from the results of the anisotropic Ginzburg-Landau theory, and the ratio of the upper critical field Hc2‖/Hc2⊥ for H‖ab and H⊥ab can both increase and decrease with temperature, depending on the relation between D1 and D2. Implications of the obtained results for MgB2 are discussed.

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