Effect of quasiparticle tunneling on quantum-phase fluctuations and the onset of superconductivity in granular films

Recent experiments on the onset of superconductivity in granular films have raised a number of interesting issues regarding the role of quantum fluctuations of the phase variable. We model the granular film as an ordered array of Josephson-coupled grains, and we take into account quasiparticle tunneling via the method of Ambegaokar, Eckern, and Schön. The onset of superconductivity, at T=0, occurs when the value of the normal-state sheet resistance has a critical value of order h/4$e^2$, which is not very sensitive to the capacitance of the grains.