Kondo effect in a one dimensional d-wave superconductor

TL;DR

This paper models the Kondo effect in a one-dimensional d-wave superconductor, revealing unique low-temperature thermodynamics and impurity behavior, with implications for understanding edge states and Majorana fermions.

Contribution

It introduces a solvable resonant-level model for impurity spins coupled to edge states in 1D d-wave superconductors, highlighting a novel two-channel Kondo effect.

Findings

Finite maximum in impurity susceptibility at zero temperature

Splitting of impurity into two Majorana fermions

Comparison with 2D d-wave superconductor Kondo effect

Abstract

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 logarithmic-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.