Topology of the Order Parameter in the Little-Parks Experiment

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Abstract
Under appropriate geometry, magnetic field, and temperature, numerical minimization of the free energy predicts a stable superconducting phase where part of the sample is normal, so that the magnetic flux is not enclosed by the superconducting part. This phase mediates between the normal phase and the superconducting phase which has been usually considered. For one point in the filed-temperature plane, it has been proven analytically that this intermediate phase minimizes the free energy. Near the transition, even when the doubly connected phase is stable, the order parameter tries to mimic that of a simply connected phase.