Duality in Josephson Junction Arrays

TL;DR

This paper reviews the duality between charges and vortices in mesoscopic 2D Josephson junction arrays, highlighting how this duality persists under external influences and extends to double-layer configurations.

Contribution

It reveals a fundamental charge-vortex duality in Josephson junction arrays and introduces a new duality in double-layer systems, expanding understanding of their topological excitations.

Findings

Charges and vortices are dual to each other.

Duality persists under magnetic fields and offset charges.

Double-layer arrays exhibit an extended duality.

Abstract

Various properties of mesoscopic two-dimensional Josephson junction arrays are reviewed. Particular attention is paid to structure of the topological excitations, charges and vortices, which are shown to be dual to each other. This duality persists in the presence of external magnetic fields and offset charges, which influence vortices and charges in an equivalent way. A double-layer junction array is also considered, where an even further reaching duality is discovered.