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 = |∆|/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, non-viscous and viscous superfluids, is proposed. For the stationary magnetic response, at vs < vL with only the non-viscous superfluid, the Meissner supercurrent is excited and the gap equation can reduce to Ginzburg-Landau equation. At vs≥vL, with the normal fluid, non-viscous and viscous superfluids, in addition to the directly excited Meissner supercurrent in the superfluid, 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 non-viscous superfluid is present whereas at vs≥vL, normal fluid, non-viscous 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.

Nonlinear optical response of collective modes in multiband superconductors assisted by nonmagnetic impurities

“…For example, H 1 is indispensable to describe linear response of dirty single-band BCS superconductors [38][39][40]. It has been predicted that this coupling would dominate also the nonlinear optical response [30][31][32][47][48][49]. In terms of the Green's function method, this is because impurity scattering produces nonvanishing Feynman diagrams that vanish in the clean limit [50].…”

Harnessing ultraconfined graphene plasmons to probe the electrodynamics of superconductors

“…Experimental detection has been achieved only through higher-order response, e.g., by pumping the superconductor with intense terahertz fields and measuring the resulting oscillations in the superfluid density (9)(10)(11)(12)(13). [It has been recently suggested, however, that the observed oscillations could be interpreted as resulting from excitation of the NG mode instead (8,(14)(15)(16)(17). Additionally, it has also been pointed out that the Higgs mode may be observed in disordered superconductors (18), as long as one chooses to measure the appropriate response function (19).…”

Lightwave terahertz quantum manipulation of nonequilibrium superconductor phases and their collective modes

“…, contain the kinetic terms in the Ginzburg-Landau equation [53]. Such spatial contributions can be expanded as in Ginzburg-Landau theory.…”