Thermal vortex creep and depinning in strong pinning theory

We study creep-type motion (due to temperature $T>0$) of vortices pinned in type-II superconductors by a low density $n_p$ of strong defects. Kramer's rate theory is used to calculate the thermal transitions between the pinned and free vortex branches characteristic for the strong pinning. In the critical drive region $j\lesssim j_c$, the steady-state branch occupation is derived as a modification of the critical (Bean) state. Transitions over the activation barrier $U(j)=\alpha e_p(1-j/j_c)^{3/2}$ ($e_p$ is the pinning potential depth and $\alpha$ a known numerical) shift the critical current, $1-j_c(T)/j_c(0)\sim (T/e_p)^{2/3}$ and smooth the current-velocity characteristic. Beyond $j_c$, $U(j)$ varies logarithmically and creep results in the shift of the $T = 0$ excess-current characteristic for drives $j<(1+\alpha') j_c(0),\, (\alpha'\propto T/n_p)$ covering a large region if $n_p$ is small. At small drives $j\sim (T/e_p)j_c$, we derive the thermally assisted flux flow (TAFF) characteristic $v = (j/j_c)v_0e^{-U_0/T}$ with activation barrier $U_0=\alpha''e_p$ governing transitions close to the thermal equilibrium. Results are supported by various experiments (Xiao et al., Phys. Rev. B 65, 094511 (2002), Palstra et al., Phys. Rev. Lett. 61, 1662 (1988)).