Gauge Theories of Josephson Junction Arrays

TL;DR

This paper models the zero-temperature behavior of planar Josephson junction arrays using an Abelian gauge theory with a Chern-Simons term, revealing a quantum phase transition and potential anyon superconductivity.

Contribution

It introduces a gauge-theoretic framework for Josephson junction arrays, connecting charge-vortex coupling, topological excitations, and phase transitions, including extensions to three dimensions.

Findings

Identifies a gauge theory governing the quantum phases of Josephson arrays.

Describes a superconductor to superinsulator transition at the self-dual point.

Explores conditions for anyon superconductivity phases with external fluxes.

Abstract

We show that the zero-temperature physics of planar Josephson junction arrays in the self-dual approximation is governed by an Abelian gauge theory with periodic mixed Chern-Simons term describing the charge-vortex coupling. The periodicity requires the existence of (Euclidean) topological excitations which determine the quantum phase structure of the model. The electric-magnetic duality leads to a quantum phase transition between a superconductor and a superinsulator at the self-dual point. We also discuss in this framework the recently proposed quantum Hall phases for charges and vortices in presence of external offset charges and magnetic fluxes: we show how the periodicity of the charge-vortex coupling can lead to transitions to anyon superconductivity phases. We finally generalize our results to three dimensions, where the relevant gauge theory is the so-called BF system, with an antisymmetric Kalb-Ramond gauge field.