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

Abstract

We report numerical calculations of a dynamic pairbreaking current density $J_d$ and a critical superfluid velocity $v_d$ in a nonequilibrium superconductor carrying a uniform, large-amplitude ac current density $J(t)=J_a\sinΩt$ with $Ω$ well below the gap frequency $Ω\ll Δ_0/\hbar$. The dependencies $J_d(Ω,T)$ and $v_d(Ω,T)$ near the critical temperature $T_c$ were calculated from either the full time-dependent nonequilibrium equations for a dirty s-wave superconductor and the time-dependent Ginzburg-Landau (TDGL) equations for a gapped superconductor, taking into account the GL relaxation time of the order parameter $τ_{GL}$ and the inelastic electron-phonon relaxation time of quasiparticles $τ_E$. We show that both approaches give similar frequency dependencies of $J_d(Ω)$ and $v_d(Ω)$ which gradually increase from their static pairbreaking GL values $J_c$ and $v_c$ at $Ωτ_E\ll 1$ to $\sqrt{2}J_c$ and $\sqrt{2}v_c$ at $Ωτ_E\gg 1$. Here $J_d$, $v_d$ 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 $H=H_a\sinΩt$ 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 $τ_E$ increases.