Topology and Phase Transitions in the Little-Parks Experiment

Details Topology and Phase Transitions in the Little-Parks Experiment Topology and Phase Transitions in the Little-Parks Experiment

1996-08-08

arxiv.org/abs/supr-con/9608001v1

SIAM J Appl Math {\bf 58} (1998) 103--121

Physics

Condensed Matter

Superconductivity

Latex, 26 pages, 5 figs upon request

Scientific paper

This is an analytic study of the problem of transitions between normal and superconducting phases for a sample which encloses a magnetic flux. A preliminary study of this problem, based on numerical minimization of the free energy for a particular form of the thickness of the sample, was published in Phys. Rev. Lett. {\bf 75}, 320 (1995). For a sample of uniform thickness the order parameter is uniform, but even infinitesimal deviations from uniform thickness give rise to a singly connected state in which the order parameter vanishes at a suitable layer, so that the superconducting part does not enclose the magnetic field. The stability domain of this singly connected 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.

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