Critical fields of superconductors with magnetic impurities

Abstract

The upper critical field Hc2, the field Hc3 for nucleation of the surface superconductivity, and the thermodynamic field Hc are evaluated within the weak-coupling theory for the isotropic s-wave case with arbitrary transport, and pair-breaking scattering. We find that, for the standard geometry of a half-space sample in a magnetic field parallel to the surface, the ratio R=Hc3/Hc2 is within the window 1.55≲R≲2.34, regardless of temperature or the scattering type. While the nonmagnetic impurities tend to flatten the R(T) variation, magnetic scattering merely shifts the maximum of R(T) to lower temperatures. Surprisingly, while reducing the transition temperature, magnetic scattering has a milder impact on R than nonmagnetic scattering. The surface superconductivity is quite robust; in fact, the ratio R≈1.7 even in the gapless state. We used Eilenberger's energy functional to evaluate the condensation energy Fc and the thermodynamic critical field Hc for any temperature and scattering parameters. By comparing Hc2 and Hc, we find that, unlike transport scattering, the pair-breaking pushes materials toward type-I behavior. We find a peculiar behavior of Fc as a function of the pair-breaking scattering parameter at the low-T transition from gapped to gapless phases, which has recently been associated with the topological transition in the superconducting density of states.

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