Title: Geometrical destruction of the global phase coherence in ultrathin superconducting cylinders

Abstract: The global phase coherence in doubly-connected superconductors leads to fluxoid quantization, allowing the superfluid velocity vs to be controlled by an applied magnetic flux. In ultrasmall samples this quantization requirement leads, surprisingly, to the destruction of the phase coherence itself around half-integer flux quanta, because of the sample-size-induced growth in vs, as predicted by de Gennes. We report observations of the predicted phenomenon in ultrathin Al and Au0.7In0.3 cylinders, and the corresponding phase diagram for ultrathin superconducting cylinders. The new phase diagram features disconnected superconducting regions, as opposed to the single one seen in the conventional Little-Parks experiment.