Rare-region onset of superconductivity in niobium nanoislands

We report measurements of the superconducting properties of isolated Nb nanoislands (600--2500 nm diameters) and explain their unusual behavior in terms of rare-region onset effects, predicted for random metal-superconductor granular systems [B. Spivak, P. Oreto, and S. A. Kivelson, Phys. Rev. B 77, 214523 (2008)]. We find that the island ${T}_c$ is strongly suppressed even at large island diameters, exceeding 1 \ensuremath{\mu}m. This behavior is unexpected given that conventional theories of superconductivity in small grains predict suppression of ${T}_c$ only at a length scale that is two orders of magnitude smaller. In addition, we observe large island-to-island variations in ${T}_c$ for nominally identical islands. These two experimental observations, coupled with direct measurement of grain distribution using transmission electron microscopy, conductive atomic force microscopy, and computer simulations, provide evidence for our picture in which the onset of superconductivity on an island coincides with the transition temperature of its largest constituent grain, and then spreads to other grains due to proximity coupling.