Design for the detection of the singly connected superconducting state

We study the Little-Parks effect for mesoscopic loops with highly nonuniform thickness. The results follow the trend of the phase diagram obtained for almost uniform thickness. In particular, the singly connected state is stable on a line segment delimited by two critical points. Most of this study considers loops with piecewise constant thickness; in this case the Euler-Lagrange equation can be integrated analytically. Under appropriate conditions, the temperature range where the singly connected state is stable is proportional to the square of the ratio between the maximal and the minimal thicknesses. Our results may serve as a guide for planning experiments. (C) 1997 Elsevier Science B.V.