Josephson critical current in a long mesoscopic S-N-S junction

Abstract

We carry out an extensive experimental and theoretical study of the Josephson effect in S-N-S junctions made of a diffusive normal metal ͑N͒ embedded between two superconducting electrodes ͑S͒. Our experiments are performed on Nb-Cu-Nb junctions with highly transparent interfaces. We give the predictions of the quasiclassical theory in various regimes on a precise and quantitative level. We describe the crossover between the short-and the long-junction regimes and provide the temperature dependence of the critical current using dimensionless units eR N The Josephson effect is well known to exist in weak links connecting two superconducting electrodes S, e.g., a tunnel barrier I, a short constriction C or a normal metal N ͑S-I-S, S-C-S, and S-N-S junctions͒. This effect manifests itself in a nondissipative dc current flowing through the Josephson junction at zero voltage. At weak coupling, e.g., in the S-I-S case, the Josephson current can be expressed as I s ϭI c sin , where is the phase difference between the two superconducting condensates and the maximum supercurrent I c is called the critical current.The Josephson effect in S-N-S junctions has been studied in a variety of configurations. The early experiments of Clarke 1 and Shepherd 2 were performed in Pb-Cu-Pb sandwiches. In these experiments and in the pioneering calculations by de Gennes, 3 it was already realized that the presence of a supercurrent in such structures is due to the proximity effect. This can be understood as the generation of superconducting correlations in a normal metal connected to a superconductor, mediated by phase-coherent Andreev reflections at the S-N interfaces. The critical current I c is limited by the ''bottleneck'' in the center of the N-layer, where the pair amplitude is exponentially small: I c ϰe ϪL/L T . Here, L T ϭͱបD/2k B T is the characteristic thermal length in the diffusive limit and L is the length of the junction. These calculations, as well as those by Fink, 4 analyzed the temperature dependence of I c within the Ginzburg-Landau theory in the vicinity of the superconducting critical temperature T c . Later, the critical current of diffusive S-N-S microbridges 5,6 was successfully described by Likharev 7 with the aid of the quasiclassical Usadel equations. 8 In this work, the emphasis was put on the high-temperature regime where the superconducting order parameter is smaller than the thermal energy ⌬Ӷk B T. A more general study of the Josephson effect in diffusive S-N-S junctions was made in Ref. 9.More recently, experimental data on long Josephson junctions 10 showed a surprising temperature dependence, which turned out to be in a strong disagreement with the early theory by de Gennes. These data have been discussed by some of us 11 within the quasiclassical approach, which we will also use in the present work. Fink 12 attempted to analyze the data 10 by means of an extrapolation of the GinzburgLandau theory to low temperatures.The proximity effect in mesoscopic hybrid structures consisting of normal and superc...

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