Kondo effect in a one-dimensional d-wave superconductor

We derive a solvable resonant-level–type model, to describe an impurity spin coupled to zero-energy bound states localized at the edge of a one-dimensional d-wave superconductor. This results in a two-channel Kondo effect with a quite unusual low-temperature thermodynamics. For instance, the local impurity susceptibility yields a finite maximum at zero temperature (but no $\ln$-divergence) due to the splitting of the impurity in two Majorana fermions. Moreover, we make comparisons with the Kondo effect occurring in a two-dimensional d-wave superconductor.