  Systems of superconducting islands placed on normal metal films offer tunable
realizations of two-dimensional (2D) superconductivity; they can thus elucidate
open questions regarding the nature of 2D superconductors and competing states.
In particular, island systems have been predicted to exhibit zero-temperature
metallic states. Although evidence exists for such metallic states in some 2D
systems, their character is not well understood: the conventional theory of
metals cannot explain them, and their properties are difficult to tune. Here,
we characterize the superconducting transitions in mesoscopic island-array
systems as a function of island thickness and spacing. We observe two
transitions in the progression to superconductivity; both transition
temperatures exhibit unexpectedly strong depression for widely spaced islands.
These depressions are consistent with the system approaching zero-temperature
metallic states. The nature of the transitions and the state between them is
explained using a phenomenological model involving the stabilization of
superconductivity on each island via a weak coupling to and feedback from its
neighbors.

Superconductivity;Mesoscale and Nanoscale Physics