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

physical review. b./physical review. b

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