Static and dynamic properties of vortices in a small Josephson-junction array

Abstract

An array consisting of 12 junctions arranged in a triangular lattice has recently been observed to exhibit quantum interference of vortices. That vortices should exist in such small arrays and exhibit classical behavior qualitatively similar to those found in larger arrays has been an important assumption for the interpretation of experimental results. We therefore investigate, using static and dynamic simulations, the classical properties of vortices in a small Josephson-junction array. By employing a relaxation technique, we find that the energy barrier, U b , preventing a single vortex from moving from the center of one array-lattice site to the next is dependent on the applied frustration ƒ, where ƒ is the number of flux quanta per unit cell. Solving the set of coupled-second order differential equations derived from the RCSJ model, we observe for f≥0.08 a vortex-flow region in the array's I-V characteristic.