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A phenomenological model F of the superconducting phase of electronic systems with strong short-range repulsive interactions is studied. Fluctuations of the connection a of an internal U (1) gauge symmetry suppress local charge fluctuations. Above H₂₁, magnetic flux can pierce the superconductor in vortices with flux hc/2e throughout the superconducting phase, but regimes are found in which the lowest-energy configuration has vortices with flux hc/e. Experiments by Little and Parks and others, which examine periodicities as a function of a varying magnetic field, always observe a period in external flux of hc/2e. The low-energy properties of a symplectic large-N expansion of a model of the CuO₂ layers of the cuprate superconductors are shown to be well described by F. This analysis and some normal-state properties of the cuprates suggest that hc/e vortices should be stable at the lowest dopings away from the insulating state at which superconductivity first occurs, unless the superconductor-normal transition is strongly first order.
Subir Sachdev (Wed,) studied this question.