Vortex motion in Josephson-junction arrays near f=0 and f=1/2.

We study vortex motion in two-dimensional Josephson arrays at magnetic fields near zero and one-half flux quanta per plaquette (f=0 and f=1/2). The array is modeled as a network of resistively and capacitively shunted Josephson junctions at temperature T=0. Calculations are carried out over a range of the McCumber-Stewart junction damping parameter \ensuremath{\beta}. Near both f=0 and f=1/2, the I-V characteristics exhibit two critical currents, ${\mathit{I}}_{\mathit{c}1}$(f) and ${\mathit{I}}_{\mathit{c}2}$(f), representing the critical current for depinning a single vortex, and for depinning the entire ground-state phase configuration. Near f=0, single vortex motion just above ${\mathit{I}}_{\mathit{c}1}$(0) leads to Josephson-like voltage oscillations. The motion of the vortex is seemingly overdamped (i.e., nonhysteretic) even when the individual junction parameters are highly underdamped, in agreement with experiments. At sufficiently large \ensuremath{\beta}, and sufficiently high vortex velocity, the vortex breaks up into a row of resistively switched junctions perpendicular to the current. Near f=1/2, the vortex potential, and corresponding vortex trajectories, are more complicated than near f=0. Nevertheless, the vortex is still ``overdamped'' even when the individual junctions are highly underdamped, and there is still row-switching behavior at large values of \ensuremath{\beta}. A high-energy vortex in a very underdamped array tends to generate resistively switched rows rather than to move ballistically. Some possible explanations for this behavior are discussed.