Vortex reflections at boundaries of Josephson junction arrays

Abstract

We study the propagation properties of a single vortex in square Josephson-junction arrays (JJA) with free boundaries and subjected to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction equations. For zero Stewart-McCumber parameter βc we find that the vortex always escapes from the array when it gets to the boundary. For βc≥2.5 and for low currents we find that the vortex escapes, while for larger currents the vortex is reflected as an antivortex at one edge and the antivortex as a vortex at the other, leading to a stationary vortex oscillatory state and to a nonzero time-averaged voltage. The escape and the reflection of a vortex at the array edges is qualitatively explained in terms of a coarse-grained model of a vortex interacting logarithmically with its image. For βc≥50 we find that the reflection regime is split up in two disconnected regimes separated by a second vortex escape regime. When considering an explicit vortex-antivortex pair in an array with periodic boundaries, we find a solitonlike nondestructive collision in virtually the same current regimes as where we find reflection of a single vortex at a free boundary; outside these current regimes the pair annihilates. We also discuss the case when the free boundaries are at 45° with respect to the current direction, and thus the angle of incidence of the vortex to the boundaries is 45°. Finally, we study the effect of self-induced magnetic fields (for penetration depths ranging from 10 to 0.3 times the lattice spacing) by taking into account the full-range inductance matrix of the array and find qualitatively equivalent results. We also discuss possible consequences of these results to experimental systems.