Optical Properties of px + ipy Superconductors with Strong Impurities

We study effects of strong impurities on the optical properties of a chiral p x + ip y superconductor with broken time-reversal symmetry. Potential impurities create subgap states in the superconductor’s spectrum similar to Yu–Shiba–Rusinov states on magnetic impurities in a conventional superconductor. We calculate the average density of states and find both the profile of the subgap impurity band due to localized states and modifications to the continuous spectrum above the gap. We also consider the anomalous Hall response of the superconductor at arbitrary frequencies and temperatures arising due to skew scattering on impurities. Hall conductivity is responsible for the polar Kerr effect and can be directly measured in an optical experiment. The frequency dependence of the Hall conductivity exhibits a rich structure corresponding to various possible transitions of quasiparticles between superconducting condensate, localized impurity states, and continuous spectrum above the gap.