Dissipation and quantum fluctuations in granular superconductivity

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, $R_S$. Most surprisingly the system is always statically disordered even in the superconducting state. For d≥2 both the dynamical response and static ordering depend sensitively on $R_S$. Specifically, for $R_S$ less than a critical value of order the quantum of resistance, h/4$e^2$, 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.