Three dimensional ordering and upper critical fields for a system of weakly coupled superconducting filaments

Abstract

We establish a theory for the three dimensional ordering at low temperature of a system of weakly coupled superconducting filaments. We take into account the phase fluctuations of the order parameter exactly and the interaction between filaments in a mean field approximation. We find that Tc varies with the strength of the coupling J as j ½ in zero external magnetic field. New properties arise from the discrete character of the system such as Tc periodic with respect to Hc2∥ with a period ϕ0/a2 and Hc2⊥ infinite for T < Tc /√2. We discuss the possibility of observing such properties in a more general case