Journal of Log' Temperature Physics, Vol. 75, Nos. 5/6, 1989 Quantum Coherence and Phase Transitions in Granular Superconductors with Dissipation. I. Ordered Arrays S. V. Panyukov and A. D. Zaikin I. E. Tamm Department of Theoretical Physics, P. N. Lebedev Physical Institute of the USSR Academy of Sciences, Moscow, USSR (Received December 20, 1988) We investigate the effect of dissipative currents on a superconducting phase transition in two- and three-dimensional granular arrays. We find the corre- sponding 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 at T= O, we find the universal critical resistance Rc only for three dimensional arrays while for two dimensional ones R~ 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 the XY model phase transition and show that strong dissipation is extremely effective in suppressing quantum effects. 1. INTRODUCTION Quantum effects in Josephson junction arrays and granular supercon- ductors may play an important role. It was shown in a number of papers (see, for instance, Refs. 1-4) that these effects should be taken into account if the grain charging energy Eo= (2e)2/C (C is the grain capacitance) is comparable with (or larger than) the Josephson coupling energy Ej between the nearest grains. In this case quantum fluctuations reduce the tendency to superconducting ordering. For rather small values of the ratio Ej/EQ, this effect leads to the absence of long-range phase coherence (and thus to the absence of superconductivity) even at T = 0. During last several years, investigations of qualitatively new macro- scopic quantum effects in single Josephson junctions are of considerable interest. For instance the effect of macroscopic quantum tunneling of the 361 oo22-2291/89/o6oo-o3615o6.oo/o © 1989PlenumPublishing Corporation