Dynamic Pair-Breaking Current in Superconductors

We calculated a dynamic pair-breaking current density $J_d$ and a critical condensate velocity $v_d$ in a thin film superconducting strip or a filament carrying a large-amplitude ac current $J(t)=J_0\sin\omega t$. Here $J_d(T,\omega)$ and $v_d(T,\omega)$ in a dirty superconductor at $T\approx T_c$ were computed by numerical simulations of the time-dependent Ginzburg-Landau (TDGL) equations, as well as the full time-dependent Usadel and kinetic equations that take into account both a nonequilibrium distribution function of quasiparticles and nonlinear current pairbreaking effects. It is shown that superconductivity is destroyed at $J_0>J_d$, where the dynamic pairbreaking current density $J_d(T,\omega)$ approaches $\sqrt{2}J_{GL}(T)$ at $\omega\tau > 1$. Here $J_{GL}(T)$ is the GL dc depairing current density and $\tau(T)$ is the energy relaxation time of quasiparticles on phonons. Nonlinear electromagnetic response of a nonequilibrium superconductor and intermodulation at $J<J_d$ were also calculated.