On the Phase Diagram of Josephson Junction Arrays with Offset Charges

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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 (σ> e) of the offset charges probability distribution; with nearest-neighbor interactions, the insulating lobe around q=e is destroyed even for small values of σ. 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.