Kondo effect in gapless superconductors

Abstract

We present a self-consistent theory of Kondo impurities in gapless unconventional superconductors valid in the Fermi-liquid regime T≲${\mathit{T}}_{\mathit{K}}$. 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${\mathrm{\Vert }}^{\mathit{r}}$, there exists a critical coupling ${\mathit{J}}_{\mathit{c}}$ below which the Kondo effect does not occur. However, for r≤1 or N=2 any finite concentration of impurities drives ${\mathit{J}}_{\mathit{c}}$→0. The theory provides microscopic support for phenomenological models of resonant impurity scattering in heavy-fermion systems.