Effects of quasiparticle dissipation on quantum fluctuations in granular superconductors

Quasiparticle dissipation in a granular superconductor is modeled by an effective nearest-neighbor capacitance C between the grains of a superconducting array. Using an expansion in 1/z, where z is the number of nearest neighbors in the array, I study the effects of quasiparticle dissipation on the transition temperature and short-range order of a granular superconductor. In agreement with experimental results, quasiparticle dissipation suppresses the quantum fluctuations in a superconducting array. If the self-capacitance of a grain is C0, then both the long-range and the short-range order of the array are enhanced as the ratio =C0/zC decreases. In disagreement with other work, the transition temperature is not reentrant for any value of. The results of this formalism, which consistently treats quantum fluctuations to first order in 1/z, should be valid in three-dimensional materials.