A superconductor-insulator transition in a one-dimensional array of Josephson junctions

TL;DR

This paper analyzes a one-dimensional Josephson junction array near the superconductor-insulator transition, establishing a sine-Gordon model in terms of quasi-charge and discussing the impact of random background charges.

Contribution

It reexamines the continuum limit and confirms the validity of the quasi-charge sine-Gordon description near the phase transition, including effects of disorder.

Findings

Validates the sine-Gordon model in the transition regime

Relates array parameters to the sine-Gordon model parameters

Discusses influence of random background charges

Abstract

We consider a one-dimensional Josephson junction array, in the regime where the junction charging energy is much greater than the charging energy of the superconducting islands. In this regime we critically reexamine the continuum limit description and establish the relationship between parameters of the array and the ones of the resulting sine-Gordon model. The later model is formulated in terms of quasi-charge. We argue that despite arguments to the contrary in the literature, such quasi-charge sine-Gordon description remains valid in the vicinity of the phase transition between the insulating and the superconducting phases. We also discuss the effects of random background charges, which are always present in experimental realizations of such arrays.