Effects of quasiparticle dissipation on quantum fluctuations in granular superconductors

Quasiparticle dissipation in a granular superconductor is modeled by an effective nearest-neighbor capacitance ΔC 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 ${\mathit{C}}_0$, then both the long-range and the short-range order of the array are enhanced as the ratio λ=${\mathit{C}}_0$/zΔC decreases. In disagreement with other work, the transition temperature is not reentrant for any value of λ. The results of this formalism, which consistently treats quantum fluctuations to first order in 1/z, should be valid in three-dimensional materials.