Vortex motion in Josephson-junction arrays nearf=0 andf=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 β. 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 β, 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 β. 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.