Nonlinear optical effects in inversion-symmetry-breaking superconductors

TL;DR

This paper investigates nonlinear optical effects in superconductors with inversion symmetry-breaking, revealing enhanced shift current and second harmonic generation responses, supported by theoretical models and potential experimental relevance.

Contribution

It demonstrates that inversion-symmetry-breaking in superconductors leads to significant nonlinear optical responses, supported by analytical and numerical models, expanding understanding of optical phenomena in such systems.

Findings

Nonlinear optical responses require inversion symmetry-breaking in superconductors.

Shift current and SHG signals are significantly larger than linear responses.

Scaling behaviors of SHG may explain recent experimental observations in cuprates.

Abstract

We study nonlinear optical responses in superconducting systems with inversion ($\mathcal{I}$) symmetry-breaking order parameters. We first show that any superconducting system with $\mathcal{I}$ and time-reversal ($\mathcal{T}$) symmetries requires an $\mathcal{I}$-breaking order parameter to support optical transitions between particle-hole pair bands. We then use a 1D toy model of an $\mathcal{I}$-breaking superconductor to numerically calculate linear and nonlinear conductivities, including shift current and second harmonic generations (SHG) responses. We find that the magnitude of the signal is significantly larger in shift current/SHG response compare to the linear response due to the matrix element effect. We also present various scaling behaviors of the SHG signal, which may be relevant to the recent experimental observation of SHG in cuprates [1]. Finally, we confirm the generality of our observations regarding nonlinear responses of $\mathcal{I}$-breaking superconductors, by analyzing other models including a 1D three-band model and 2D square lattice model.