Dynamic pair-breaking current, critical superfluid velocity, and nonlinear electromagnetic response of nonequilibrium superconductors

Abstract

We report numerical calculations of a dynamic pair-breaking current density Jd and a critical superfluid velocity vd in a nonequilibrium superconductor carrying a uniform, large-amplitude AC current density J(t)=JasinΩt with Ω well below the gap frequency Ω≪Δ0/ℏ. The dependencies Jd(Ω,T) and vd(Ω,T) near the critical temperature Tc were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor or the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter τGL and the inelastic electron-phonon relaxation time of quasiparticles τE. We show that both approaches give similar frequency dependencies of Jd(Ω) and vd(Ω) which gradually increase from their static pair-breaking GL values Jc and vc at ΩτE≪1 to 2Jc and 2vc at ΩτE≫1. Here Jd, vd and a dynamic superheating field at which the Meissner state becomes unstable were calculated in two different regimes of a fixed AC current and a fixed AC superfluid velocity induced by the applied AC magnetic field H=HasinΩt in a thin superconducting filament or a type-II superconductor with a large GL parameter. We also calculated a nonlinear electromagnetic response of a nonequilibrium superconducting state, particularly a dynamic kinetic inductance and a dissipative quasiparticle conductivity, taking into account the oscillatory dynamics of superconducting condensate and the kinetics of quasiparticles driven by a strong AC current. It is shown that an AC current density produces multiple harmonics of the electric field, the amplitudes of the higher-order harmonics diminishing as τE increases.

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