Unified Transport and Susceptibility Analysis of a Thin BSCCO Film: From Local Pairing to Global Phase Coherence

RESUMO

The superconducting transition in thin high-$T_c$ films can be significantly broadened by disorder, spatial inhomogeneity, and phase fluctuations. Here, we study the transition in a 30-nm-thick sputter-grown Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) film through electrical-transport and ac-susceptibility measurements. The resistive transition is examined using a Gaussian distribution of local $T_c$ values and the Ambegaokar--Halperin model, describing spatial variations in superconductivity and thermally activated phase dynamics, respectively. To relate the transport and magnetic responses, we extend the Choy--Stoneham susceptibility model by introducing the superconducting fraction extracted from transport and a temperature-dependent connectivity factor representing the gradual development of Josephson coupling among superconducting regions. The results identify separate temperature regimes corresponding to the onset of local superconductivity, expansion of the superconducting fraction, development of magnetic screening, and establishment of global phase coherence. The transition therefore proceeds progressively, from locally superconducting regions to a connected, phase-coherent state. This analysis provides a common framework for relating spatial inhomogeneity, dissipative phase dynamics, and magnetic screening in inhomogeneous superconducting films.