Vortex motion and vortex-friction coefficient in triangular Josephson-junction arrays

Abstract

We study the dynamical response of triangular Josephson-junction arrays, modeled as a network of resistively and capacitively shunted junctions. 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. The upper current corresponds either to row-switching events accompanied by steplike jumps in the array resistance, or to a depinning of the entire array. 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 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 0.042Ic, independent of the direction of applied current, in agreement with static calculations by Lobb 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.

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