Disorder induced non-Fermi liquid near a metal-superconductor quantum phase transition

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We study the flux-driven superconductor-metal transition in ultrasmall cylinders observed experimentally by Liu et.al.(Science 294, 2332 (2001)). Where Tc→ 0, there is a quantum critical point, and a large fluctuation conductivity is observed in the proximate metallic phase over a wide range of T and flux. However, we find that the predicted (Gaussian) fluctuation conductivity in the neighborhood of the quantum critical point is 4 orders of magnitude smaller than observed experimentally. We argue that the breakdown of Anderson's theorem at any non-integer flux leads to a broad fluctuation region reflecting the existence of ``rare regions'' with local superconducting order. We calculate the leading order correction to the conductivity within a simple model of statistically induced Josephson coupled local ordered regions that rationalizes the existing data.