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

Abstract 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 /4 e 2 R t ≫1) to a dirty thin metal film with dimensionless conductance g ≫1. Electrons in the film interact repulsively with the dimensionless strength λ . 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 ln b c /d∼G t 2 /λg . The critical distance b c is much less than the 2 d localization length L loc ∼ e π 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, ln b c /d∼ g .