Destruction of the global phase coherence in ultrathin, doubly connected superconducting cylinders

In doubly connected superconductors, such as hollow cylinders, the fluxoid is known to be quantized, allowing the superfluid velocity to be controlled by an applied magnetic flux and the sample size. The sample-size-induced increase in superfluid velocity has been predicted to lead to the destruction of super-conductivity around half-integer flux quanta. We report transport measurements in ultrathin Al and Au_0.7In_0.3 cylinders verifying the presence of this destructive regime characterized by the loss of the global phase coherence and reveal a phase diagram featuring disconnected phase coherent regions, as opposed to the single region seen in larger superconducting cylinders studied previously.