Frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor with impurities

TL;DR

This paper investigates how impurity scattering affects the frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor, providing theoretical insights and experimental comparisons.

Contribution

It introduces models for impurity effects on Hall conductivity in chiral superconductors and predicts their frequency and temperature behaviors, including Kerr angle estimations.

Findings

Hall conductivity is finite at zero frequency

Singularities occur at photon absorption threshold

Conductivity saturates at zero temperature

Abstract

We calculate frequency and temperature dependence of the anomalous ac Hall conductivity induced by impurity scattering in a chiral px+ipy superconductor, such as Sr2RuO4, with spontaneous time-reversal-symmetry breaking in the absence of an external magnetic field. We consider two models of disorder, Gaussian and non-Gaussian, characterized by the second and third moments of the random impurity potential, respectively. Within both models, we find that the anomalous Hall conductivity has a finite real value at zero frequency, exhibits singularities at the threshold of photon absorption across the superconducting gap, and decays as some power of the high frequency \Omega. The Hall conductivity increases linearly with the decrease of temperature below the superconducting transition and saturates at zero temperature. Using our results for the high-frequency Hall conductivity, we estimate the polar Kerr angle for light reflection from the material and compare it with the experimental measurements in Sr2RuO4 by Xia et al., Phys. Rev. Lett. 97, 167002 (2006).