Overscreening of magnetic impurities in $d_{x^2-y^2}$ wave superconductors

TL;DR

This paper investigates how magnetic impurities behave in d-wave superconductors, revealing a quantum phase transition to an overscreened Kondo state and providing diagnostic tools based on impurity properties.

Contribution

It develops an effective multichannel Kondo model for d-wave superconductors and characterizes the quantum phase transition and scaling laws of impurity properties.

Findings

Identification of a quantum phase transition at critical coupling J_c.

Derivation of scaling laws for susceptibility and specific heat.

Characterization of the overscreened Kondo phase behavior.

Abstract

We consider the screening of a magnetic impurity in a $d_{x^2-y^2}$ wave superconductor. The properties of the $d_{x^2-y^2}$ state lead to an unusual behavior in the impurity magnetic susceptibility, the impurity specific heat and in the quasiparticle phase shift which can be used to diagnose the nature of the condensed state. We construct an effective theory for this problem and show that it is equivalent to a multichannel (one per node) non-marginal Kondo problem with linear density of states and coupling constant J. There is a quantum phase transition from an unscreened impurity state to an overscreened Kondo state at a critical value J_c which varies with $\Delta_0$, the superconducting gap away from the nodes. In the overscreened phase, the impurity Fermi level $\epsilon_f$ and the amplitude $\Delta$ of the ground state singlet vanish at J_c like $\Delta_0 \exp(- const. / \Delta)$ and J-J_c respectively. We derive the scaling laws for the susceptibility and specific heat in the overscreened phase at low fields and temperatures.