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

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.