Model for small superconducting variable-thickness bridge constrictions

We present a simple model to simulate small three-dimensional superconducting constrictions of variable thickness (VTBs) for which the cross-sectional dimensions are of the same order as the length, and both are less than xi(T). We study the behavior of the modulus of the order parameter f and the supercurrent density J/sub s/ as a function of the various dimensions. We find that the extent to which f is depressed in the banks depends on the ratio of width to length of the constriction. We show that even for very abrupt geometries, J/sub s/ is not zero and f does not reach its equilibrium value immediately outside the constriction. On the basis of our results, we propose a more general expression for the effective length valid also when all dimensions are of the same order. The calculated values of dI/sub c//dT are consistent with experimental data from well-characterized VTBs. We suggest that the discrepancy between the calculated and experimental values of I/sub c/R/sub n/ may be due to the nonuniformity of the normal current density in the constriction