GINZBURG-LANDAU THEORY FOR 3-DIMENSIONAL JOSEPHSON-JUNCTION ARRAYS

We have derived a mean-field theory and a Ginzburg-Landau (GL) theory for classical three-dimensional Josephson junction arrays. We show tha t the full GL theory for arrays is formally equivalent to the GL theor y for a bulk superconductor, demonstrating that for low fields and clo se to the critical temperature, the two systems are electrodynamically equivalent. We derive expressions for the penetration depth and coher ence length, the effective superfluid density, critical fields, and th e current-phase relationship for arrays. Using the Ginzburg criterion, we show that the critical region is very wide and that three-dimensio nal critical fluctuations should be experimentally accessible. Althoug h the wide critical region casts doubt on the strict validity of the G L theory, suitable modifications of the coefficients should allow it t o be used at lower temperatures, as is done for bulk superconductors.