Approaching zero-temperature metallic states in mesoscopic superconductor{--}normal{--}superconductor arrays

Systems of superconducting islands placed on normal metal films offer tunable realizations of two-dimensional (2D) superconductivity1,2; 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 states3–5. Although evidence exists for such metallic states in some 2D systems6,7, their character is not well understood: the conventional theory of metals cannot explain them8, and their properties are difficult to tune7,9. 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, consistent with the system approaching zerotemperature (T=0) metallic states. In particular, the first transition temperature seems to linearly approach T = 0 for finite island spacing. The nature of the transitions is explained using a phenomenological model involving the stabilization of superconductivity on each island via a coupling to its neighbours. Conventional zero-temperature (T = 0) metallic states do not exist in 2D systems possessing any disorder, because of Anderson localization8,9. To reconcile this fact with experimental evidence for T = 0 metals in 2D, it has been proposed that the experimental observations do not pertain to conventional metals, but rather to spatially inhomogeneous superconducting (or, more generally, correlated) states3,4,10. Inhomogeneity is thought to arise in some of these systems because of phase separation; however, it can also be tunably engineered, for example, in hybrid superconductor– normal–superconductor (SNS) systems, such as the arrays studied here. In arrays of SNS junctions, the diffusion of electron pairs from the superconductor into the normal metal11–13—known as the proximity effect—gives rise to global superconductivity, through a transition typically described using the phenomenological theory of Lobb, Abraham and Tinkham (LAT)14. According to the LAT theory, the T = 0 state is always superconducting, and no zerotemperature metallic state should appear. Most previous studies of SNS arrays used islands much larger than the superconducting coherence length ξSC (that is, having well-defined superconductivity)1; however, there is evidence that arrays of mesoscopic islands (that is, islands of dimensions comparable to ξSC) exhibit behaviour that deviates from the LAT theory5,15, and might therefore possess non-superconducting T = 0 states. Furthermore, the dependence of the superconducting transition on key parameters—such as island spacing and size—has