Dependence of global superconductivity on inter-island coupling in arrays of long SNS junctions

We present measurements of the superconducting transition temperature, Tc, for arrays of mesoscopic Nb islands patterned on Au films, for large island spacings d. We show that Tc ∼ 1/d(2), and explain this dependence in terms of the quasiclassical prediction that the Thouless energy, rather than the superconducting gap, governs the inter-island coupling at large spacings. We also find that the temperature dependence of the critical current, Ic(T), in our arrays is similar to that of single SNS junctions. However, our results deviate from the quasiclassical theory in that Tc is sensitive to island height, because the islands are mesoscopic.