Orbital effect of Cooper pairs on the Kondo effect in unconventional superconductors

Abstract

A type of Kondo effect peculiar to unconventional superconductors is studied theoretically by using Wilson's numerical renormalization group method. In this case, the angular momentum of a Cooper pair plays an important role in the Kondo effect. It produces multichannel exchange couplings with a local spin. Here we focus on a ${p}_{x}{+ip}_{y}$-wave state which is a full-gap system. The calculated impurity susceptibility shows that the local spin is almost quenched by the Kondo effect in the strong-coupling region ${(T}_{\mathrm{K}}/\ensuremath{\Delta}\ensuremath{\rightarrow}\ensuremath{\infty}),$ while the ground state is always a spin doublet over all the ${T}_{\mathrm{K}}/\ensuremath{\Delta}$ region. Here ${T}_{\mathrm{K}}$ and $\ensuremath{\Delta}$ are the Kondo temperature and the superconducting energy gap, respectively. This is different from the s-wave pairing case where the Kondo singlet is realized for large ${T}_{\mathrm{K}}/\ensuremath{\Delta}$ values. The strong-coupling analysis shows that the ${p}_{x}{+ip}_{y}$-wave Cooper pair is connected to the Kondo singlet via the orbital dynamics of the paired electrons, generating the spin of the ground state. This type of Kondo effect reflects the symmetry of the conduction electron system.