We present results from an extensive analysis of the dynamic response of Josephson-junction arrays driven by external currents of the form I=${\mathit{I}}_{\mathrm{dc}}$+${\mathit{I}}_{\mathrm{ac}}$sin(2πνt). The dynamics is given by the resistively shunted Josephson-junction model with Johnson noise. We find a stationary axisymmetric-coherent-vortex state (ACVS) away from equilibrium and above a minimum lattice size (∼20×20) whenever the initial state has at least one antivortex and a vortex. The ACVS is characterized by tilted rows of oscillating positive and negative vortices, produced by the combined effect of the driving current plus the collective coupling of the nonlinear Josephson oscillators. The ACVS is manifested in the current-voltage characteristics as giant half-integer Shapiro steps, leading to period-two resonances in the spectral function. The stability and properties of the ACVS are studied as a function of frequency, temperature, disorder, edge magnetic fields, and lattice sizes. It is found that the ACVS is a very robust two-dimensional dynamical state that is produced under very diverse circumstances. A connection between the ACVS and half-integer steps seen in proximity effect arrays in zero field is also discussed.

• Received 26 July 1993

DOI:https://doi.org/10.1103/PhysRevB.48.13717