Ginzburg-Landau theory for three-dimensional Josephson junction arrays

Abstract

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