Description
We present a general formalism for the electromagnetic response of superconductors with finite-momentum pairing and arbitrary nonmagnetic disorder. Based on Nambu’s method and including disorder scattering, we treat the collective fluctuations of the superconducting order parameter (phase and amplitude) together with the charge-density mode on an equal footing within the BCS framework. Applied to single-band s- and d-wave superconductors on a two-dimensional lattice, the formalism reproduces the clean-limit signatures of finite-momentum pairing and continuously connects to Mattis-Bardeen theory in the dirty limit. Finite-momentum pairing generically mixes phase, amplitude and density fluctuations, and enables collective-mode contributions to optical response. Besides, in the relatively clean regime, it can imprint quasiparticle density-of-states features on the optical conductivity. Disorder influences collective-mode fluctuations, smears interband features, and in some cases enhances the visibility of certain modes. Our unified, gauge-invariant framework provides a basis to interpret linear optical experiments on superconductors across ranges of purity and pairing symmetry.
