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

We present measurements of the superconducting transition temperature, T_c, for arrays of mesoscopic Nb islands patterned on Au films, for large island spacings d. We show that T_c ∼ 1/d², 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, I_c (T), in our arrays is similar to that of single SNS junctions. However, our results deviate from the quasiclassical theory in that T_c is sensitive to island height, because the islands are mesoscopic.