Nonlinear Magneto-Optical Response of $s$- and $d$-Wave Superconductors

TL;DR

This paper investigates the nonlinear magneto-optical Kerr effect in $s$- and $d$-wave superconductors, highlighting how surface effects and mixed pairing states influence observable optical responses, especially in high-temperature superconductors.

Contribution

It provides a systematic symmetry analysis including singlet-triplet mixing induced by spin-orbit coupling, revealing new observable effects in nonlinear magneto-optical responses.

Findings

Interference of singlet and triplet states affects Kerr effect.

Surface sensitivity influences nonlinear optical response.

Results applicable to high-Tc superconductor symmetry discussions.

Abstract

The nonlinear magneto-optical response of $s$- and $d$-wave superconductors is discussed. We carry out the symmetry analysis of the nonlinear magneto-optical susceptibility in the superconducting state. Due to the surface sensitivity of the nonlinear optical response for systems with bulk inversion symmetry, we perform a group theoretical classification of the superconducting order parameter close to a surface. For the first time, the mixing of singlet and triplet pairing states induced by spin-orbit coupling is systematically taken into account. We show that the interference of singlet and triplet pairing states leads to an observable contribution of the nonlinear magneto-optical Kerr effect. This effect is not only sensitive to the anisotropy of the gap function but also to the symmetry itself. In view of the current discussion of the order parameter symmetry of High-T$_c$ superconductors, results for a tetragonal system with bulk singlet pairing for various pairing symmetries are discussed.