Doping dependence of the critical current in Bi2Sr2CaCu2Oy

The doping dependence of the critical current density, $J_c$, was measured in a series of high quality c-axis oriented $\mathrm{B}{\mathrm{i}}_2\mathrm{S}{\mathrm{r}}_2\mathrm{C}\mathrm{a}\mathrm{C}{\mathrm{u}}_2{\mathrm{O}}_{8+\delta }$ thin films. For each doping level we measured the temperature dependence of $J_c$. We find that all samples have the same temperature dependence, but the critical current at zero temperature, $J_c(0)$, has a non-trivial doping dependence with a maximum at a unique doping level in the overdoped side of the superconducting dome.