Self-Consistent Mean-Field Theory for Frustrated Josephson Junction Arrays

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We review the self-consistent mean-field theory for charge-frustrated Josephson junction arrays. Using <cos(ϕ)> (ϕis the phase of the superconducting wavefunction) as order parameter and imposing the self-consistency condition, we compute the phase boundary line between the superconducting region (<cos(ϕ)> not equal to zero) and the insulating one (<cos(ϕ)> = 0). For a uniform offset charge q=e the superconducting phase increases with respect to the situation in which q=0. Here, we generalize the self-consistent mean-field theory to include the effects induced by a random distribution of offset charges and/or of diagonal self-capacitances. For most of the phase diagram, our results agree with the outcomes of Quantum Monte Carlo simulations as well as with previous studies using the path-integral approach.