Universal Lower Limit on Vortex Creep in Superconductors

In high-temperature superconductors, creep (the rate of thermally-activated vortex motion, $\textit{S}$) considerably limits the current carrying capacity. The magnitude of $\textit{S}$ is thought to somehow positively correlate with the Ginzburg number ($\textit{Gi}$), which depends on the critical temperature ($\textit{T}_c$) and material-specific length scales. Early measurements of $\textit{S}$ in iron-based superconductors unveiled rates comparable to YBa$_2$Cu$_3$O$_{7-\delta}$, which was puzzling given that $\textit{Gi}$ is orders of magnitude lower in iron-based superconductors. Here, we report very slow creep in BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ films and evince the efficacy of BaZrO$_3$ inclusions in reducing $\textit{S}$ at high fields. We propose that there is a universal minimum realizable $S \sim Gi^{\frac{1}{2}}(\frac{T}{T_c})$ , and show that it has been achieved in our films, a few other superconductors, and violated by none. This hard constraint has two broad implications: first, the creep problem in high-$\textit{T}_c$ superconductors cannot be fully eliminated and there is a limit to how much it can be ameliorated, and secondly, we can confidently predict that any yet-to-be-discovered high-$\textit{T}_c$ superconductor will have fast creep.