BIFURCATION-ANALYSIS FOR PHASE-TRANSITIONS IN SUPERCONDUCTING RINGS WITH NONUNIFORM THICKNESS

We perform an analytic study of the problem of transitions between nor mal and superconducting phases for a sample which encloses a magnetic flux, as in the classic Little-Parks experiment. For a sample of unifo rm thickness the order parameter is uniform, but even infinitesimal de viations from uniform thickness give rise to a mixed state which avoid s enclosing the magnetic field. The stability domain of this mixed sta te is a line segment in the magnetic field-temperature plane, delimite d by two critical points. The phase diagram contains several bifurcati on lines, which are systematically analyzed.