Constraints on the orbital flux phase in $A$V$_3$Sb$_5$ from polar Kerr effect

TL;DR

This paper investigates the orbital flux phases in $A$V$_3$Sb$_5$ Kagome metals, analyzing their symmetry and optical responses to clarify the origins of observed Kerr effects and charge density wave order.

Contribution

It identifies which orbital flux orders can produce Kerr effects and predicts large Kerr rotations at specific frequencies, aiding interpretation of experimental results.

Findings

Star-of-David flux order does not produce Kerr effect.

Tri-hexagonal flux phase shows significant Kerr rotation near 1 eV.

Resonance enhancement suggests large Kerr signals at certain optical frequencies.

Abstract

The $A$V$_3$Sb$_5$ ($A=$ K, Rb, Cs) family of Kagome metals hosts unconventional charge density wave order whose nature is still an open puzzle. Accumulated evidences point to a time-reversal symmetry breaking orbital flux phase that carries loop currents. Such an order may support anomalous Hall effect. However, the polar Kerr effect measurements that probe the a.c. anomalous Hall conductivity seems to have yielded contradictory results. We first argue on symmetry grounds that some previously proposed orbital flux order, most notably the one with Star-of-David distortion, shall not give rise to anomalous Hall or polar Kerr effects. We further take the tri-hexagonal orbital flux phase as an exemplary Kagome flux order that does exhibit anomalous Hall response, and show that the Kerr rotation angle at two relevant experimental optical frequencies generally reaches microradians to sub-milliradians levels. A particularly sharp resonance enhancement is observed at around $\hbar \omega =1$ eV, suggesting exceedingly large Kerr rotation at the corresponding probing frequencies not yet accessed by previous experiments. Our study can help to interpret the Kerr measurements on $A$V$_3$Sb$_5$ and to eventually resolve the nature of their CDW order.