Effect of impurities on the superheating field of type-II superconductors

We consider the effect of nonmagnetic and magnetic impurities on the superheating field H-s in a type-II superconductor. We solved the Eilenberger equations, which take into account the nonlinear pairbreaking of Meissner screening currents, and calculated H-s (T) for arbitrary temperatures and impurity concentrations in a single-band s-wave superconductor with a large Ginzburg-Landau parameter. At low temperatures, nonmagnetic impurities suppress a weak maximum in H-s (T), which has been predicted for the clean limit, resulting, instead, in a maximum of H-s as a function of impurity concentration in a moderately clean limit. It is shown that nonmagnetic impurities weakly affect H-s even in the dirty limit, while magnetic impurities suppress both H-s and the critical temperature T-c. The density of quasiparticles states N(epsilon) is strongly affected by an interplay of impurity scattering and current pairbreaking. We show that a clean superconductor at H = H-s is in a gapless state, but a quasiparticle gap epsilon(g) in N(epsilon) at H = H-s appears as the concentration of nonmagnetic impurities increases. As the nonmagnetic scattering rate a increases above alpha(c) = 0.36, the quasiparticle gap epsilon(g) (alpha) at H = H-s increases, approaching epsilon(g) approximate to 0.32 Delta(0) in the dirty limit alpha >> 1, where Delta(0) is the superconducting gap parameter at zero field. The effects of impurities on H-s can be essential for the nonlinear surface resistance and superconductivity breakdown by strong RF fields.