Superconductor-Insulator Transition in - and Two-Dimensional Arrays of Dissipative Small Josephson Junctions

We studied one- (1D) and two-dimensional (2D) arrays of small Josephson junctions in which each junction was shunted by a normal metal resistor. For the arrays with the charging energy E_C comparable to the Josephson coupling energy E_J, we find a crossover from insulating to superconducting behavior as the shunt resistance R_S decreases. The critical value of R_S is close to dR_Q (d: dimensionality, R_Q≡h/4e² = 6.45 kΩ), which is consistent with theories of the dissipation-driven phase transition. We discuss the difference between the phase diagrams in the E_J/E_C - R_Q/R_S plane for 1D and 2D arrays.