Vortex Motion and Vortex Friction Coefficient in Triangular Josephson Junction Arrays

TL;DR

This paper investigates vortex dynamics and friction in triangular Josephson junction arrays, revealing how vortex friction depends on system parameters and modeling energy loss mechanisms, with implications for quantum effects in vortex motion.

Contribution

It extends understanding of vortex motion in triangular JJAs by modeling vortex friction and energy loss, aligning with experimental and static calculation results.

Findings

Flux flow regime extends between depinning and critical currents.

Vortex friction coefficient depends on the McCumber-Stewart parameter.

Model predictions agree with low-density vortex behavior.

Abstract

The dynamical response of triangular JJA is investigated using the RCSJ model. A flux flow regime is found to extend between a lower vortex-depinning current and a higher critical current, in agreement with previous calculations for square arrays. In the flux flow regime, the dynamical response to the bias current is roughly Ohmic, and the time-dependent voltage can be well understood in terms of vortex degrees of freedom. The vortex friction coefficient $\eta$ depends strongly on the McCumber-Stewart parameter $\beta$, and at large $\beta$ is approximately independent of the shunt resistance $R$. To account for this, we generalize a model of Geigenm\"{u}ller {\it et al} to treat energy loss from moving vortices to the phase analog of optical spin waves in a triangular lattice. The value of $\eta$ at all values of $\beta$ agrees quite well with this model in the low-density limit. The vortex depinning current is estimated as $0.042I_c$, independent of the direction of applied current, in agreement with static calculations by Lobb {\it et al}. A simple argument suggests that quantum effects in vortex motion may become important when the flux flow resistivity is of order $h/(2e)^2$ per unit frustration.