Flux-Flow and Fluctuation Effects in Granular Superconducting Films

Results are reported on the flux-flow state in granular aluminum films. Anomalously small values of depinning current are reported and attributed to the fact that the temperature-dependent coherence length is appreciably larger than the grain size in these films. Near $T_c$, the energy dissipated in vortex flow $D (D\propto \frac{d{\rho }_f}{\mathrm{dH}}$, where ${\rho }_f$ is the flow resistivity) was found to vary exponentially with temperature. This anomalous temperature dependence suggests that the major source of energy dissipation in this regime is the interaction of the vortex current fields with thermodynamic fluctuations. For sufficiently large values of $\frac{R_{\square }^N}{\epsilon }$ [$R_{\square }^N=\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}-\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t}\mathrm{e}$ resistance per square and $\epsilon =\frac{(T_c-T)}{T_c}$], the ${\rho }_f-\mathrm{v}\mathrm{s}-H$ curves were found to be non-linear in a manner not reported before in conventional flux-flow experiments. This curvature is attributed to the above-mentioned interaction between the vortices and fluctuations.