Global and local phase coherence in dissipative josephson-junction arrays

It is shown that at zero temperature a regular network of Josephson junctions in one or two dimensions including quantum fluctuations and dissipation has three different phases: A nonsuperconducting one with no order in the phases of locally superconducting grains and two different superconducting ones showing either long-range spatial phase coherence and a Meissner effect or local phase coherence only. The latter phase occurs for normal state sheet resistances smaller than 6.5 kΩ and may explain the corresponding observed threshold for superconductivity in thin granular films.