MEAN-FIELD THEORY FOR ARRAYS OF JOSEPHSON-COUPLED WIRES

We describe a mean-field theory for phase transitions in a Josephson j unction array consisting of two sets of parallel wire networks, arrang ed at right angles and coupled together by Josephson interactions. In contrast to earlier treatments, we include the variation of the superc onducting phase along the individual wires; such variation is always p resent if the wires have finite thickness and are sufficiently long. T he mean-field result is obtained by treating the individual wires exac tly and the coupling between them within the mean-field approximation. For a perpendicular applied magnetic field of strength f=p/q flux qua nta per plaquette (where p and q are mutually prime integers), we find that the mean-field transition temperature T-c(f) approximate to T-c( 0)q(-b) with b=1/4. By contrast, a mean-field theory which neglects ph ase variation along the array predicts b=1/2, and gives a T-c which di verges in the thermodynamic limit. The model with phase variations agr ees somewhat better with experiment on large arrays than does the appr oximation which neglects phase variations. [S0163-1829(98)07138-0].