Giant Shapiro steps with screening currents

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Abstract
We present a detailed study of the dynamic response of overdamped Josephson-junction square arrays driven by a dc plus ac current, including self-induced magnetic-field effects, as a function of a parameter κ. The transition from type-II (κ>1) to type-I (κIV characteristics show fractional giant Shapiro steps, with and without external magnetic fields, with microscopic coherent vortex dynamics fundamentally different in the two extreme κ limits. Our results in zero external magnetic field are in good agreement with recent experiments in Nb-Au-Nb arrays.