On a least upper bound Tc of superconductors with paramagnetic impurities

Abstract

We have obtained a least upper bound, k BT c ⩽ c(μ ∗, t)A , on the critical temperature T c of an isotropic superconductor with paramagnetic impurities described by the scattering matrix t for fixed values of μ ∗. We have also obtained the corresponding optimal spectrum α 2F(m) = Aδ[ω−d(μ ∗, A] . The numerical results for the functions c(μ ∗, t) and d(μ ∗, t) are presented for α ∗ = 0.1 and 0.16 in the form of universal curves representing c(μ ∗, t) and d(μ ∗, t) as functions of the reduced impurity concentration t = t/A . We have also established an upper limit to the reduced critical concentration t crit for an arbitrary shape of α 2 F( ω)1.