Mean Field Theory of Josephson Junction Arrays with Charge Frustration

TL;DR

This paper derives the phase boundary equation for quantum Josephson junction arrays with charge frustration using path integral methods, revealing reentrant behavior and providing a Ginzburg-Landau free energy formulation.

Contribution

It offers an explicit derivation of phase boundary equations and Ginzburg-Landau free energy for arrays with charge frustration and complex capacitance matrices, including reentrant phenomena.

Findings

Reentrant phase boundary behavior observed with short-range interactions.

Explicit charge distribution configurations for lowest energy states.

Path integral approach yields elegant derivation of free energy.

Abstract

Using the path integral approach, we provide an explicit derivation of the equation for the phase boundary for quantum Josephson junction arrays with offset charges and non-diagonal capacitance matrix. For the model with nearest neighbor capacitance matrix and uniform offset charge $q/2e=1/2$, we determine, in the low critical temperature expansion, the most relevant contributions to the equation for the phase boundary. We explicitly construct the charge distributions on the lattice corresponding to the lowest energies. We find a reentrant behavior even with a short ranged interaction. A merit of the path integral approach is that it allows to provide an elegant derivation of the Ginzburg-Landau free energy for a general model with charge frustration and non-diagonal capacitance matrix. The partition function factorizes as a product of a topological term, depending only on a set of integers, and a non-topological one, which is explicitly evaluated.