  The critical behavior of disordered systems-from metals (1) to magnets (2)
and superconductors (3)-is often dominated by the behavior of rare regions of a
correlated phase, which control the inception and dynamics of the phase
transition. Yet, despite significant theoretical (3,4,5) and experimental
(6,7,8,9) interest, there has been little direct evidence of the presence of
these regions, or of their role in initiating transitions. Here, we provide
direct evidence for rare-region effects at the onset of superconductivity in
granular superconducting islands. By considering the strong diameter-dependence
of the transition, as well as observations of large fluctuations in the
transition temperature as island diameters decrease, we are able to show that
superconducting order first appears in unusually large grains- i.e. rare
regions- within each island and, due to proximity coupling, spreads to other
grains. This work thus provides a quantitative, local understanding of the
onset of correlated order in strongly disordered systems.
