Dynamic Penetration Field of Vortices in a Superconductor in a Time-Dependent Magnetic Field

We address the nonlinear dynamics of penetration of vortices in a superconductor subject to a periodic magnetic field $H(t)=H_0\sin\omega t$ parallel to the surface. The time-dependent Ginzburg-Landau equations for a gapped superconductor were simulated numerically to calculate the frequency and temperature dependencies of the field onset $H_p(T,\omega)$ of vortex penetration at $T\approx T_c$. It is shown that $H_p(T,\omega)$ can exceed the dc superheating field $H_{s}$ at which the Meissner state becomes unstable. Here $H_p(T,\omega)$ increases with $\omega$ and approaches $\sqrt{2}H_{s}(T)$ at $\omega\tau\geq 1$, where $\tau(T)$ is the energy relaxation time of quasiparticles on phonons. We also investigated the effect of surface topographic defects on $H_p(T,\omega)$ and showed that they can substantially reduce $H_p(T,\omega)$ and cause additional power dissipation.