How do I go from the eigenvalues (band structure) and eigenvectors of a 2D superconductor to its optical conductivity?

In the supplementary information of this Ni et al. paper "Plasmons in graphene moiré superlattices", we have a "Kubo formula" that’s used to obtain the optical conductivity of a non-superconducting system from its energy values and eigenspinors (as a function of the angular frequency of light).

Does any such formula exist that can be generalized to superconductors (whose optical response is heavily dominated by their strongly diamagnetic nature)?

Essentially, I have in hand a matrix of eigenvalues and eigenvectors for each point in my hypothetical superconducting system’s momentum space, and from these, I need the system’s optical conductivity as a function of angular frequency of light.