Superconductor-insulator transition in Josephson junction arrays screened by a superconducting ground plane

We have studied quantum phase transitions in unconventional Josephson arrays with a large number of interacting nearest-neighbour islands (typically, 10). The range of inter-island interactions was controlled by the presence/absence of a superconducting ground plane placed in close proximity to the array. We have found that the superconductor-to-insulator transition occurs in the arrays with both short- and long-range interactions at $E_{J}/E_{C}\sim1$ . Here $E_{J}$ is the effective Josephson energy per island, $E_{C}$ is its charging energy. However, the critical resistance for the arrays with short-range interactions greatly exceeds the quantum resistance, in contrast to the case of arrays with long-range interactions. These experiments clearly show that the ratio $E_{J}/E_{C}$ is the only relevant (for the SIT) parameter, while the critical resistance can vary a great deal depending on the interaction range.