Temperature dependence of critical currents in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ ceramics

The temperature dependence of critical currents in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ superconducting ceramics have been studied following the Ginzburg-Landau theory and the de Gennes proximity effects for a superconductor–normal-conductor interface. Based on an S/N/S weak-link model, critical currents as a function of temperature have been calculated and a model able to describe different kinds of ${\mathit{I}}_{\mathit{c}}$-T characteristics in 1:2:3 ceramics has been developed. A set of four ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ ceramic samples has been prepared for experimental studies. These samples were annealed under different conditions. Critical currents as a function of temperature have been measured in a high-heat-transfer system. ${\mathit{I}}_{\mathit{c}}$-T characteristics ranging from a quadratic temperature dependence to a temperature dependence of the Josephson-tunneling type have been observed. The experimental ${\mathit{I}}_{\mathit{c}}$-T characteristics fit very well theoretical predictions which include the effects of randomness in the thickness of the nonsuperconducting barriers and the boundary conditions for the samples.