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Nanostructuring of superconducting materials to form dense arrays of thinparallel nanowires with significantly large transverse Josephson coupling hasproven to be an effective way to increase the upper critical field ofsuperconducting elements by as much as two orders of magnitude as compared tothe corresponding bulk materials and, in addition, may cause considerableenhancements in their critical temperatures. Such materials have been realizedin the linear pores of mesoporous substrates or exist intrinsically in the formof various quasi-1D crystalline materials. The transverse coupling between thesuperconducting nanowires is determined by the size-dependent coherence lengthE0. In order to obtain E0 over the Langer-Ambegaokar- McCumber-Halperin (LAMH)theory, extensive experimental fitting parameters have been required over thelast 40 years. We propose a novel Monte Carlo algorithm for determining E0 ofthe multi-Cooper pair system in the 1D limit. The concepts of uncertaintyprinciple, Pauli-limit, spin flip mechanism, electrostatic interaction, thermalperturbation and co-rotating of electrons are considered in the model. We usePb nanowires as an example to monitor the size effect of E0 as a result of themodified electron-electron interaction without the need for experimentalfitting parameters. We investigate how the coherence length determines thetransverse coupling of nanowires in dense arrays. This determines whether ornot a global phase-coherent state with zero resistance can be formed in sucharrays. Our Monte Carlo results are in very good agreement with experimentaldata from various types of superconducting nanowire arrays

physica c superconductivity

Electron-electron interactions of the multi-Cooper-pairs in the 1D limit  and their role in the formation of global phase coherence in  quasi-one-dimensional superconducting nanowire arrays