Theory of optical responses in clean multiband superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a momentum-non-conserving theory by Mattis and Bardeen for over 60 years. In this talk, we establish the conditions for nonzero intrinsic momentum-conserving optical excitations. We find that multi-band effects are essential, additionally, one of the following three conditions is required: (i) inversion symmetry breaking, (ii) the emergence of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling. We apply our theory to optical responses in FeSe.