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

Department of Physics and Astronomy, Lehman College, City University of New York 250 Bedford Park Boulevard West, Bronx, NY 10468-1589, USA

Received: 26 May 2016
Accepted: 29 July 2016

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 , 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 the dependence of the persistent current on disorder and computed numerically agrees quantitatively with the analytical result derived within the spin-wave approximation. The high- 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.