Dissipation and quantum fluctuations in granular superconductivity

Abstract

The effects of dissipation and quantum fluctuations on the onset of superconductivity are discussed. A model for a granular superconductor is considered which consists of a d-dimensional array of resistively shunted Josephson junctions with charging energy incorporating the long-ranged Coulomb interaction. In one dimension the model exhibits a T=0 dynamical transition into a state with vanishing resistivity at a critical value of the shunt resistance, RS. Most surprisingly the system is always statically disordered even in the superconducting state. For d2 both the dynamical response and static ordering depend sensitively on RS. Specifically, for RS less than a critical value of order the quantum of resistance, h/4e2, the dissipation suppresses quantum fluctuations enabling the array to order at T=0 for arbitrarily weak Josephson coupling. Above this critical resistance and for weak coupling, the order parameter suffers phase slips due to quantum tunneling driving the system normal. © 1987 The American Physical Society.