Anomalous Hall conductivity of clean Sr2RuO4 at finite temperatures

Building on previous work, we calculate the temperature- and frequency-dependent anomalous Hall conductivity for the putative multiband chiral superconductor Sr2RuO4 using a simple microscopic two-orbital model without impurities. A Hall effect arises in this system without the application of an external magnetic field due to the time-reversal-symmetry breaking chiral superconducting state. The anomalous Hall conductivity is nonzero only when there is more than one superconducting order parameter, involving inter- as well as intra-band Cooper pairing. We find that such a multiband superconducting state gives rise to a distinctive resonance in the frequency-dependence of the Hall conductivity at a frequency close to the inter-orbital hopping energy scale that describes hopping between Ru dxz and dyz orbitals. The detection of this feature, robust to temperature and impurity effects in the superconducting phase, would thus constitute compelling evidence in favour of a multiband origin of superconductivity in Sr2RuO4, with strong superconductivity on the α and β bands. The temperature dependence of the Hall conductivity and Kerr rotation angle are studied within this model at the one-loop approximation.