On the Phase Diagram of Josephson Junction Arrays with Offset Charges

We study the effects of external offset charges on the phase diagram of Josephson junction arrays. Using the path integral approach, we provide a pedagogical derivation of the equation for the phase boundary line between the insulating and the superconducting phase within the mean-field theory approximation. For a uniform offset charge q=e the superconducting phase increases with respect to q=0 and a characteristic lobe structure appears in the phase diagram when the critical line is plotted as a function of q at fixed temperature. We review our analysis of the physically relevant situation where a Josephson network feels the effect of random offset charges. We observe that the Mott-insulating lobe structure of the phase diagram disappears for large variance (\sigma > e) of the offset charges probability distribution; with nearest-neighbor interactions, the insulating lobe around q=e is destroyed even for small values of \sigma. Finally, we study the case of random self-capacitances: here we observe that, until the variance of the distribution reaches a critical value, the superconducting phase increases in comparison to the situation in which all self-capacitances are equal.