Influence of Fermi Surface Geometry and Van Hove Singularities on the Optical Response of Sr$_2$RuO$_4$

TL;DR

This paper investigates how Fermi surface geometry and Van Hove singularities affect the optical Hall response and Kerr effect in Sr$_2$RuO$_4$, revealing the importance of orbital symmetries and Lifshitz transitions.

Contribution

It introduces a three-orbital model analyzing the influence of Fermi surface features on optical responses and identifies key orbital symmetries relevant for Kerr effect observations.

Findings

Chiral $p$-wave state in quasi-1D orbitals is crucial for Kerr angle.

Lifshitz transition causes sharp changes in $T_c$ and optical transport.

Inter-orbital charge transfer modifies the balance of orbital contributions.

Abstract

Motivated by the sensitivity of Sr$_2$RuO$_4$ to Fermi surface reconstructions under strain, we investigate how Fermi surface geometry and Van Hove singularities influence the optical Hall response and polar Kerr effect. Within a three-orbital model, we explore the impact of chemical potential and interlayer hopping on superconducting pairing and response functions. We find that $d_{x^2-y^2}$ and $d_{x^2-y^2}+ig$ symmetries are the leading candidates for the quasi-2D orbital, while a chiral $p$-wave state in the quasi-1D orbitals is essential for generating an accessible Kerr angle. The Lifshitz transition is shown to affect coherence factors and density-of-states peaks, producing sharp signatures in $T_c$ and optical transport. Inter-orbital charge transfer further enhances these effects by modifying the balance between quasi-1D and quasi-2D contributions. These results provide a framework for interpreting Kerr effect experiments in multi-orbital superconductors.