Effects of Geometric Phases in Josephson Junction Arrays

TL;DR

This paper investigates how geometric phases influence vortex dynamics in Josephson junction arrays, revealing zero classical Hall effect and complex quantum Hall behaviors due to quantum geometric effects.

Contribution

It demonstrates the negligible classical Magnus force and predicts complex quantum Hall effects arising from geometric phases in Josephson junction arrays.

Findings

Classical Magnus force component is effectively zero.

Zero Hall effect predicted in the classical limit.

Rich quantum Hall behaviors analogous to known topological effects.

Abstract

We show that the en route vortex velocity dependent part of the Magnus force in a Josephson junction array is effectively zero, and predict zero Hall effect in the classical limit. However, geometric phases due to the finite superfluid density at superconductor grains have a profound influence on the quantum dynamics of vortices. Subsequently we find rich and complex Hall behaviors analogous to the Thouless-Kohmoto-Nightingale-den Nijs effect in the quantum regime.