Bifurcation Analysis for Phase Transitions in Superconducting Rings with Nonuniform Thickness

Abstract

We perform an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux, as in the classic Little--Parks experiment. For a sample of uniform thickness the order parameter is uniform, but even infinitesimal deviations from uniform thickness give rise to a mixed state which avoids enclosing the magnetic field. The stability domain of this mixed state is a line segment in the magnetic field-temperature plane, delimited by two critical points. The phase diagram contains several bifurcation lines, which are systematically analyzed.