Nonlinear Viscous Vortex Motion in Two-Dimensional Josephson-Junction Arrays

TL;DR

This paper investigates the nonlinear viscous motion of vortices in two-dimensional Josephson junction arrays, revealing a velocity-dependent viscosity model that explains current-voltage behavior in the damped regime.

Contribution

It introduces a nonlinear viscous force model for vortex motion in Josephson arrays, supported by numerical simulations and applicable to different lattice geometries.

Findings

Current-voltage characteristics are described by a nonlinear viscous force model.

The nonlinear friction law applies to both square and triangular lattices.

Qualitative analysis provides insight into microscopic vortex dynamics.

Abstract

When a vortex in a two-dimensional Josephson junction array is driven by a constant external current it may move as a particle in a viscous medium. Here we study the nature of this viscous motion. We model the junctions in a square array as resistively and capacitively shunted Josephson junctions and carry out numerical calculations of the current-voltage characteristics. We find that the current-voltage characteristics in the damped regime are well described by a model with a {\bf nonlinear} viscous force of the form $F_D=\eta(\dot y)\dot y={{A}\over {1+B\dot y}}\dot y$, where $\dot y$ is the vortex velocity, $\eta(\dot y)$ is the velocity dependent viscosity and $A$ and $B$ are constants for a fixed value of the Stewart-McCumber parameter. This result is found to apply also for triangular lattices in the overdamped regime. Further qualitative understanding of the nature of the nonlinear friction on the vortex motion is obtained from a graphic analysis of the microscopic vortex dynamics in the array. The consequences of having this type of nonlinear friction law are discussed and compared to previous theoretical and experimental studies.