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

Abstract

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 vs is larger than a threshold vL=|Δ|/kF. 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. For the stationary magnetic response, at vs<vL with only the nonviscous superfluid, the Meissner supercurrent is excited and the gap equation can be reduced to the Ginzburg-Landau equation. At vs≥vL, with the normal fluid and nonviscous and viscous superfluids, in addition to the directly excited Meissner supercurrent in the superfluid, a normal-fluid current is also induced through the friction drag with the viscous superfluid current. Due to the normal-fluid and viscous-superfluid currents, the penetration depth is influenced by the scattering effect. In addition, a modified Ginzburg-Landau equation is proposed. We predict an exotic phase in which both the resistivity and superconducting gap are finite. As for the optical response, the excited vs oscillates with time. When vs<vL, only the nonviscous superfluid is present, whereas at vs≥vL, normal fluid and nonviscous and viscous superfluids are present. We show that the excited normal-fluid current exhibits the Drude-model behavior, while the superfluid current consists of the Meissner supercurrent and Bogoliubov quasiparticle current. Due to the friction between the superfluid and normal-fluid currents, the optical conductivity is captured by the three-fluid model. Finally, we also study the optical excitation of the Higgs mode. By comparing the contributions from the drive and Anderson-pseudospin pump effects, we find that the drive effect is dominant at finite temperature whereas at zero temperature, both effects contribute.

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