Molecular-field approximation for Josephson-coupled superconducting arrays in a magnetic field

Abstract

A molecular-field approximation is developed for two-dimensional or three-dimensional Josephson- or proximity-coupled superconducting arrays in an applied magnetic field. The molecular-field transition temperature ${T}_{c}(H)$ is found to map onto the highest energy of an electron in a tight-binding band in the presence of a magnetic field (a problem treated by Hofstadter). ${T}_{c}(H)$ is thus periodic in $H$ with complex substructure, some of which has been observed experimentally.