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

TL;DR

This paper develops a self-consistent mean-field theory to analyze phase transitions in charge-frustrated Josephson junction arrays, incorporating randomness in offset charges and capacitances, and validates results against quantum Monte Carlo simulations.

Contribution

It generalizes existing mean-field theory to include effects of random offset charges and capacitances, providing a comprehensive phase diagram analysis.

Findings

Superconducting phase increases with uniform offset charge q=e.

Results agree with Quantum Monte Carlo simulations.

Phase boundary line computed using self-consistent mean-field approach.

Abstract

We review the self-consistent mean-field theory for charge-frustrated Josephson junction arrays. Using <cos(\phi)> (\phi is 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(\phi)> not equal to zero) and the insulating one (<cos(\phi)> = 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.