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Within a gauge-invariant microscopic kinetic theory, we study theelectromagnetic response in the superconducting states. Both superfluid andnormal-fluid dynamics are involved. We predict that the normal fluid is presentonly when the excited superconducting velocity $v_s$ is larger than a threshold$v_L=|\Delta|/k_F$. Interestingly, with the normal fluid, we find that thereexists friction between the normal-fluid and superfluid currents. Due to thisfriction, part of the superfluid becomes viscous. Therefore, a three-fluidmodel: normal fluid, non-viscous and viscous superfluids, is proposed. For thestationary magnetic response, at $v_s<v_L$ with only the non-viscoussuperfluid, the Meissner supercurrent is excited and the gap equation canreduce to Ginzburg-Landau equation. At $v_s{\ge}v_L$, with the normal fluid,non-viscous and viscous superfluids, in addition to the directly excitedMeissner supercurrent in the superfluid, normal-fluid current is also inducedthrough the friction drag with the viscous superfluid current. Due to thenormal-fluid and viscous superfluid currents, the penetration depth isinfluenced by the scattering effect. In addition, a modified Ginzburg-Landauequation is proposed. We predict an exotic phase in which both the resistivityand superconducting gap are {\em finite}. As for the optical response, theexcited ${v_s}$ oscillates with time. When $v_s<v_L$, only the non-viscoussuperfluid is present whereas at $v_s{\ge}v_L$, normal fluid, non-viscous andviscous superfluids are present. We show that the excited normal-fluid currentexhibits the Drude-model behavior while the superfluid current consists of theMeissner supercurrent and Bogoliubov quasiparticle current. Due to the frictionbetween the superfluid and normal-fluid currents, the optical conductivity iscaptured by the three-fluid model.

Gauge-invariant microscopic kinetic theory of superconductivity in response to electromagnetic fields