Vortex Motion and Vortex Friction Coefficient in Triangular Josephson Junction Arrays

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 $η$ depends strongly on the McCumber-Stewart parameter $β$, and at large $β$ is approximately independent of the shunt resistance $R$. To account for this, we generalize a model of Geigenmüller {\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 $η$ at all values of $β$ 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.