Anomalous Hall conductivity of clean Sr2RuO4 at finite temperatures

TL;DR

This paper calculates the anomalous Hall conductivity in Sr2RuO4, revealing a multiband superconducting state with a distinctive resonance feature that could confirm its multiband nature.

Contribution

It introduces a microscopic two-orbital model to analyze the temperature- and frequency-dependent Hall conductivity without impurities, highlighting a resonance linked to inter-orbital hopping.

Findings

Resonance in Hall conductivity near inter-orbital hopping energy

Hall effect arises without external magnetic field due to chiral superconductivity

Robust temperature and impurity effects support multiband superconductivity evidence

Abstract

Building on previous work, we calculate the temperature- and frequency-dependent {\it anomalous} Hall conductivity for the putative multiband chiral superconductor $\Sr$ 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 $d_{xz}$ and $d_{yz}$ 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 $\Sr$, with strong superconductivity on the $\alpha$ and $\beta$ bands. The temperature dependence of the Hall conductivity and Kerr rotation angle are studied within this model at the one-loop approximation.