Systematic study of doping-dependent critical current density in Bi₂Sr₂CaCu₂O8+δ via repetitive annealing on a single crystal

The doping dependence of the critical current density ( J c ) in a Bi 2 Sr 2 CaCu 2 O 8+ δ single crystal was studied via magnetization measurements following repeated post-annealing on the same crystal. At high temperatures, where vortex lines are pinned, J c increased monotonically with hole concentration (p). In contrast, at low temperatures, where pancake vortices are pinned, J c exhibited two distinct peaks at p ~ 0.12 and p ~ 0.17. These results indicate that different pinning mechanisms dominate in each regime. The low-temperature two peaks suggest inhomogeneous superconductivity, likely induced by electronic and/or structural modifications near these doping levels.