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

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We show that an isolated impurity in a spin singlet dₓ₂₋y₂ superconductor generates a dxy order parameter with locally broken time-reversal symmetry. The origin of this effect is a coupling between the dₓ₂₋y₂ and the dxy 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 dxy component, discuss its spatial structure as well as the pattern of induced current and local magnetic field near the localized impurity spin.