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

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 $T^{\ast }=\sqrt{2JU}$, 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 $T^{\ast }\ll J$ the dependence of the persistent current on disorder and $T^{\ast }$ computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high-$T^{\ast }$ 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.

6 pages, 5 figures

References in corpus (9)

• Direct coupling between magnetism and superconducting current in Josephson Phi junction
• Magnetic moment manipulation by a Josephson current
• Collective transport in the insulating state of Josephson junction arrays
• Superconductor-insulator transition in nanowires and nanowire arrays
• An inhomogeneous Josephson phase in thin-film and High-Tc superconductors
• Quantum Monte Carlo study of a magnetic-field-driven 2D superconductor-insulator transition
• Continuous phase transition of a fully frustrated XY model in three dimensions
• Instanton Glass Generated by Noise in a Josephson-Junction Array
• Quantum decay of the persistent current in a Josephson junction ring