Magnetic Impurities in d-wave Superconductors

TL;DR

This paper investigates how magnetic impurities affect d-wave superconductors, revealing conditions for local magnetic moments and the emergence of time-reversal symmetry breaking states with complex current patterns.

Contribution

It introduces a variational approach to analyze magnetic impurities in d-wave superconductors and uncovers the conditions for local moment formation and induced complex superconducting states.

Findings

Local magnetic moments form only if the normal state Kondo temperature exceeds the maximum gap.

Non-zero spin-orbit coupling induces a time-reversal breaking state around the impurity.

Current patterns around the impurity are explicitly calculated.

Abstract

We solve the problem of a magnetic impurity in a $d_{x^2-y^2}$-wave superconductor by a variational method. A moment is found to exist in the superconducting state only if the Kondo-temperature in the normal state is larger than the maximum in the superconducting gap-function. If a moment exists in the superconducting state, and provided spin-orbit coupling is non-zero, it induces a time-reversal breaking superconducting state locally around the inpurity which is a linear combination of the $d_{x^2-y^2}$ and $d_{xy}$ states. The current pattern around the impurity in this state are evaluated.