Vortex reflection at boundaries of Josephson-junction arrays

TL;DR

This paper investigates how vortices behave at the boundaries of Josephson-junction arrays, revealing conditions for vortex escape, reflection, and stationary states influenced by array parameters and boundary orientations.

Contribution

It provides a detailed analysis of vortex boundary interactions in Josephson-junction arrays, including effects of array parameters, boundary angles, and magnetic fields, with a new coarse-grained interaction model.

Findings

Vortices escape at boundaries for zero Stewart-McCumber parameter.

Vortex reflection occurs at higher Stewart-McCumber parameters and low currents.

Boundary orientation and magnetic fields influence vortex dynamics and stationary states.

Abstract

We study the propagation properties of a single vortex in square Josephson-junction arrays (JJA) with free boundaries and subject to an applied dc current. We model the dynamics of the JJA by the resistively and capacitively shunted junction (RCSJ) equations. For zero Stewart-McCumber parameter $\beta_c$ we find that the vortex always escapes from the array when it gets to the boundary. For $\beta_c\geq 2.5$ 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 oscillatory state and to a non-zero time-averaged voltage. The escape and the reflection of a vortex at the array edges are qualitatively explained in terms of a coarse-grained model of a vortex interacting logarithmically with its image. We also discuss the case when the free boundaries are at $45$ degrees with respect to the direction of the vortex motion. Finally, we discuss the effect of self-induced magnetic fields by taking into account the full-range inductance matrix of the array, and find qualitatively equivalent results.