Quantum superconductor-metal transition in a 2D proximity-coupled array

We construct a theory of quantum fluctuations in a regular array of small superconductive islands of size d connected via low-resistance tunnel contacts (G(t) = h/4e R-2(t) much greater than 1) to a dirty thin metal film with dimensionless conductance g much greater than 1. Electrons in the film interact repulsively with the dimensionless strength lambda. The system is macroscopically superconductive when the distance b between neighbouring islands is short enough. The zero-temperature phase transition from the superconductive to the normal-conductive state is shown to occur with the increase of distance between superconductive islands, at In b(c)/d similar to G(t)(2)/lambda g. The critical distance b(c) is much less than the 2d localization length L-loc similar to e(pi g), so the considered effect develops when weak-localization corrections are still small. The T-c(g, b) dependence at b < b(c) is found. These results are valid at sufficiently large g, whereas a decrease of g is expected to lead eventually to another b(c)(g) dependence, In b(c)/d similar to root g. (C) 1998 Elsevier Science B.V. All rights reserved.