Gauge-invariant microscopic kinetic theory of superconductivity in response to electromagnetic fields I: Application to current excitation

Within a gauge-invariant microscopic kinetic theory, we study the electromagnetic response in the superconducting states. Both superfluid and normal-fluid dynamics are involved. We predict that the normal fluid is present only when the excited superconducting velocity is larger than a threshold. Interestingly, with the normal fluid, we find that there exists friction between the normal-fluid and superfluid currents. Due to this friction, part of the superfluid becomes viscous. Therefore a three-fluid model, normal fluid and nonviscous and viscous superfluids, is proposed to capture both the magnetic and optical responses. Moreover, an exotic phase in which both the resistivity and superconducting gap are finite is predicted.