Magnetic impurities in<i>d</i>-wave superconductors

Abstract

We solve the problem of a magnetic impurity in a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-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 nonzero, it induces a time-reversal breaking superconducting state locally around the inpurity which is a linear combination of the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{\mathrm{xy}}$ states. The current pattern around the impurity in this state is evaluated.