Persistent current in a 2D Josephson junction array wrapped around a cylinder

TL;DR

This paper investigates persistent currents in a 2D Josephson junction array on a cylinder, revealing how disorder, temperature, and quantum phase transitions affect current behavior through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of persistent currents in a 2D Josephson junction array, connecting quantum statistical mechanics with classical spin models and exploring vortex effects.

Findings

Persistent current depends on disorder and effective temperature, matching analytical spin-wave results.

High effective temperature and disorder lead to vortex loop dominance and current suppression.

Quantum phase transition destroys persistent current, indicating a transition to the insulating phase.

Abstract

We study persistent currents in a Josephson junction array wrapped around a cylinder. The $T=0$ quantum statistical mechanics of the array is equivalent to the statistical mechanics of a classical $xy$ spin system in 2+1 dimensions at the effective temperature $T^{*}=\sqrt{2JU}$, with $J$ being the Josephson energy of the junction and $U$ being the charging energy of the superconducting island. It is investigated analytically and numerically on lattices containing over one million sites. For weak disorder and $T^{*}\ll J$ the dependence of the persistent current on disorder and $T^{*}$ computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high-$T^{*}$ and/or strong-disorder behavior is dominated by instantons corresponding to the vortex loops in 2+1 dimensions. The current becomes destroyed completely at the quantum phase transition into the Cooper-pair insulating phase.