Quantum Hall Fluid of Vortices in a Two Dimensional Array of Josephson Junctions

TL;DR

This paper demonstrates that vortices in a 2D Josephson junction array can form a quantum Hall fluid, leading to quantized electronic transport, with unique properties due to the bosonic nature of vortices.

Contribution

It introduces the concept of a quantum Hall fluid of vortices in Josephson junction arrays and analyzes its distinct properties compared to electronic quantum Hall fluids.

Findings

Vortices behave like electrons in a magnetic field on a 2D lattice.

A quantum Hall fluid of vortices can form under certain conditions.

The vortex quantum Hall fluid results in quantized Hall electronic transport.

Abstract

A two dimensional array of Josephson junctions in a magnetic field is considered. It is shown that the dynamics of the vortices in the array resembles that of electrons on a two--dimensional lattice put in a magnetic field perpendicular to the lattice. Under appropriate conditions, this resemblance results in the formation of a quantum Hall fluid of vortices. The bosonic nature of vortices and their long range logarithmic interaction make some of the properties of the vortices' quantum Hall fluid different from those of the electronic one. Some of these differences are studied in detail. Finally, it is shown that a quantum Hall fluid of vortices manifests itself in a quantized Hall electronic transport in the array.