Coherent and paracoherent states in Josephson-coupled granular superconductors

The order parameter of an assembly of superconducting grains of diameter greater than the coherence length is a set of vectors in the complex plane. It is shown that if the grains are coupled through the Josephson effect, the system is the analog of a Heisenberg ferromagnet with spin dimensionality 2. A phase transition occurs from a paracoherent state to a coherent one above and below, respectively, a coherent temperature To < T c. It is only in the latter domain of temperatures, where superconducting phases are ordered, that Josephson effects will be fully displayed by the system as a whole. Approximate equations of motion are derived and thereby effects due to phase fluctuations upon the DC characteristics are studied theoretically and experimentally. The systems obey London electrodynamics and possess peculiar quantum interference properties