Quantum coherence and phase transitions in granular superconductors with dissipation. I. Ordered arrays

Abstract

We investigate the effect of dissipative currents on a superconducting phase transition in two- and three-dimensional granular arrays. We find the corresponding phase diagrams and show that, depending on dissipation, both long-range and local quantum fluctuations may be effective in destroying the global phase coherence. For large values of charging-to-Josephson coupling energy ratio and atT=0, we find the universal critical resistanceRc only for three dimensional arrays while for two dimensional onesR c −1 diverges logarithmically with increasing of the grain charging energy. For large values of a Josephson coupling energy, quantum phase slip effects play the main role and lead to the universal critical resistance in both cases. We also investigate the effect of dissipation on the critical temperature of theXY model phase transition and show that strong dissipation is extremely effective in suppressing quantum effects.