Sum rule of the optical activity in noncentrosymmetric superconductors

Optical responses in superconductors have provided important insights since the first observation of the superconducting gap in 1956 using far-infrared rays. For example, the optical spectrum has contributed to identifying the gap symmetry and the measurement of the superfluid density and the penetration length using the Ferrell-Glover-Tinkham (FGT) sum rule.

In this presentation, we focus on the optical activity. The optical activity originates from the spatial dispersion of the optical conductivity, exhibiting the optical rotation, the dichroism, and the birefringence. These effects are ubiquitous and have been widely observed from chiral molecules to noncentrosymmetric solids, however, theoretical studies have been mainly carried out in molecular systems and the research in solids has not developed to the same level. The band theory of the optical activity has been developed in some works, revealing the correspondence with the molecular systems through the multipole theory in solids, applying to various systems including chiral crystals, twisted bilayer graphenes, and a topological antiferromagnet, and allowing the evaluation by the first-principles calculation.

While the theoretical studies in the normal phase have gradually progressed, the research in superconductors remains largely unexplored. In this presentation, we discuss the general properties of the optical activity in superconductors. We show a sum rule of the optical activity, and the summation is independent of the materials' details. Furthermore, the spectrum reduced by the superconducting gap results in a missing area, which is absorbed by the delta function in the DC limit corresponding to the superconducting Edelstein effect (SEE). The measurement of the missing area makes it possible to exactly evaluate the SEE, which has not been observed in experiments, due to the obtained universal sum rule. This discussion extends the FGT sum rule to the optical activity.