Signatures for the second critical point in the phase diagram of a superconducting ring

We study the Little-Parks effect for families of mesoscopic loops with highly nonuniform thickness, using a recently developed formalism which predicts a phase diagram with two critical points at half-integer number of magnetic flux quanta. The Euler-Lagrange equation can be integrated analytically, and this feature provides an easy way to locate the second critical point and evaluate the derivative of the supercurrent. The derivative of the supercurrent (ac susceptibility) has been recently measured. Our results and experiments share the same qualitative features.