Mean-field theory for Josephson junction arrays with charge frustration

We derive, using a finite-temperature path integral approach, the equation for the phase boundary between the insulating and the superconducting phase for quantum Josephson junctions arrays (JJA’s) with offset charges and general capacitance matrices. We show that—within the mean field theory approximation—a reentrance in the phase boundary should appear, for systems with a uniform distribution of offset charges, only when the capacitance matrix is nondiagonal. For a model with nearest-neighbor capacitance matrix and uniform offset charge q/2e=1/2, we find reentrant superconductivity even if the intergrain interaction is short ranged; for this model, we determine the most relevant contributions to the equations for the phase boundary by explicitly constructing the charge distributions on the lattice corresponding to the lowest-energy states which provide the leading contributions to the partition function at low T_c.