Spin and orbital effects of Cooper pairs coupled to a single magnetic impurity

Abstract

The Kondo effect strongly depends on spin and orbital degrees of freedom of unconventional superconductivity. We focus on the Kondo effect in uniformly gapped superconducting systems (the two-dimensional ${p}_{x}{+ip}_{y}$-wave and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$-wave superconductors here) to compare the magnetic properties of the spin-triplet and spin-singlet Cooper pairs. The difference appears when both of the paired electrons couple to a local spin directly. For the ${p}_{x}{+ip}_{y}$ wave, the ground state is always a spin doublet for a ${S}_{\mathrm{imp}}=1/2$ local spin, and it is always a spin singlet for ${S}_{\mathrm{imp}}=1.$ The latter is due to uniaxial spin anisotropy of the triplet Cooper pair. For the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}{+id}_{\mathrm{xy}}$ wave, the interchange of ground states occurs, which resembles a competition between the Kondo effect and the superconducting energy gap in s-wave superconductors. Thus the internal degrees of freedom of Cooper pairs give a variety to the Kondo effect.