Kondo effect in gapless superconductors

We present a self-consistent theory of Kondo impurities in gapless unconventional superconductors valid in the Fermi-liquid regime T{}TK. The impurity degrees of freedom are treated using the large-N slave-boson technique, leading to tractable equations describing the interplay between the Kondo effect and superconductivity. We show that for a single impurity in a superconductor with density of states N({ω}){~}{}{ω}ʳ, there exists a critical coupling Jc below which the Kondo effect does not occur. However, for r{≤}1 or N=2 any finite concentration of impurities drives Jc{→}0. The theory provides microscopic support for phenomenological models of resonant impurity scattering in heavy-fermion systems.