We have studied two-dimensional superconducting networks coupled by Josephson junctions in the regime where the Josephson coupling energy is comparable in magnitude to the capacitive energy of charging an island with a Cooper pair. We have mapped out the dependence of quantum phase transitions on the ratio of these two energies ͑for different values of the applied magnetic field͒ and on the applied field for arrays both with square and triangular cells. Our experimental results are compared with existing theoretical predictions.

We have studied phase transitions in fabricated 2D arrays of Josephson junctions where the charging and Josephson coupling energies are about equal. We find a crossover from superconducting behavior in low fields to insulating behavior for fields above a critical value of 0.1-0.2 flux quanta per unit cell. The quantitative aspects agree well with predictions from a recent theory for quantum vortex motion by M. P. A. Fisher and with measurements on films. Similar transitions are found around values /=/i/m, where/is the flux per cell and «,w = 1,2,3. The field dependence is periodic in/with period 1.

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