Local Time-Reversal Symmetry Breaking in d_(x2-y2) Superconductors

TL;DR

This paper demonstrates that impurities in d_{x2-y2} superconductors can induce a local d_{xy} order parameter that breaks time-reversal symmetry, leading to observable magnetic effects.

Contribution

It provides a microscopic theory showing how impurity-induced spin-orbit scattering creates a local d_{xy} component and associated magnetic phenomena in d_{x2-y2} superconductors.

Findings

Impurity induces a d_{xy} order parameter with broken time-reversal symmetry.

Localized orbital charge current generates a magnetic field near the impurity.

The spatial structure of the induced current and magnetic field is characterized.

Abstract

We show that an isolated impurity in a spin singlet d_{x2-y2} superconductor generates a d_{xy} order parameter with locally broken time-reversal symmetry. The origin of this effect is a coupling between the d_{x2-y2} and the d_{xy} order parameter induced by spin-orbit scattering off the impurity. The signature of locally broken time-reversal symmetry is an induced orbital charge current near the impurity, which generates a localized magnetic field in the vicinity of the impurity. We present a microscopic theory for the impurity induced d_{xy} component, discuss its spatial structure as well as the pattern of induced current and local magnetic field near the localized impurity spin.