Kerr effect from diffractive skew scattering in chiral $p_x \pm i p_y$ superconductors

TL;DR

This paper calculates the temperature-dependent anomalous ac Hall conductance in a chiral p-wave superconductor, revealing impurity-induced contributions that are crucial for understanding the Kerr effect observed in Sr$_2$RuO$_4$.

Contribution

It identifies and explicitly computes impurity-induced extrinsic contributions to the Hall response, highlighting their importance in interpreting Kerr effect measurements.

Findings

Impurity-induced skew scattering significantly affects the Hall conductance.

Previously overlooked contributions are shown to be leading order in impurity concentration.

Results are relevant for understanding Kerr effect experiments in chiral superconductors.

Abstract

We calculate the temperature dependent anomalous ac Hall conductance $\sigma_H(\Omega, T)$ for a two-dimensional chiral p-wave superconductor. This quantity determines the polar Kerr effect, as it was observed in Sr$_2$RuO$_4$ [J. Xia $et$ $al.$, Phys. Rev. Lett. 97, 167002 (2006)]. We concentrate on a single band model with arbitrary isotropic dispersion relation subjected to rare, weak impurities treated in the Born approximation. As we explicitly show by detailed computation, previously omitted contributions to extrinsic part of an anomalous Hall response, physically originating from diffractive skew scattering on quantum impurity complexes, appear to the leading order in impurity concentration. By direct comparison with published results from the literature we demonstrate the relevance of our findings for the interpretation of the Kerr effect measurements in superconductors.