Unique properties of the optical activity in noncentrosymmetric superconductors: sum rule, missing area, and relation with the superconducting Edelstein effect

TL;DR

This paper explores the optical activity in noncentrosymmetric superconductors, deriving a sum rule and linking the missing spectral area to the superconducting Edelstein effect, providing a new experimental observation method.

Contribution

It establishes a universal sum rule for optical activity in superconductors and connects the missing spectral area to the superconducting Edelstein effect, which has not been observed before.

Findings

Sum rule of optical activity spectrum is zero, independent of electric states.

Superconducting phase exhibits a delta-function singularity in optical activity.

Missing spectral area in superconductors relates to the Edelstein effect.

Abstract

We present general properties of the optical activity in noncentrosymmetric materials, including superconductors. We derive a sum rule of the optical activity in general electric states and show that the summation of the spectrum is zero, which is independent of the details of electric states. The optical activity has a $\delta$-function singularity that vanishes in normal phases. However, the singularity emerges in superconducting phases, corresponding to the Meissner effect in the optical conductivity. The spectrum decreases by the superconducting gap and has a missing area compared to the normal phase. This area is exactly equivalent to the coefficient of the $\delta$-function singularity due to the universal sum rule. Furthermore, the coefficient is exactly equivalent to the superconducting Edelstein effect, which has not yet been observed in experiments. Thus, this measurement of the missing area offers an alternative way to observe the superconducting Edelstein effect.