Frequency dependence of the intrinsic Hall conductivity in a chiral $p+ip$ superconductor with impurities

We calculate frequency dependence of the intrinsic Hall conductivity induced by impurity scattering in a chiral $p_x+ip_y$ superconductor. We find that, at large frequencies compared to the superconducting gap ($\Omega\gg\Delta$), the real part of the intrinsic Hall conductivity at zero temperature is proportional to $\Delta/\Omega^3\log(\Omega/2\Delta)$. Using our results for the Hall conductivity, we estimate the Kerr angle and compare it with the experimental data on $\rm Sr_2RuO_4$ by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).