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

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 Ω. 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).

arXiv comment22 pages, 12 figures;

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• Origin of the anomalous Hall effect in two-band chiral superconductors
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• Whether there is the intrinsic Hall effect in a multi-band superconductor?
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• Impact of random impurities on the anomalous Hall effect in chiral superconductors
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• Quantum-geometry-induced anomalous Hall effect in nonunitary superconductors and application to Sr${}_2$RuO${}_4$
• Necessity of Time-Reversal Symmetry Breaking for the Polar Kerr Effect in Linear Response
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• Fluctuational Anomalous Hall and Nernst Effects in Superconductors
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• Probing time reversal symmetry breaking topological superconductivity in twisted double layer copper oxides with polar Kerr effect
• Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr${}_2$RuO${}_4$