Influence of induced magnetic fields on Shapiro steps in Josephson-junction arrays

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Abstract
Using numerical simulation, we study the effect of self-induced magnetic fields on the properties of Josephson-junction arrays driven with combined ac and dc currents. We show that inductive effects in strongly overdamped arrays can induce subharmonic giant Shapiro steps in zero applied magnetic field. Inductive effects can also reduce the range of dc current biases over which the array can lock to the ac current. Calculation of the correct current-voltage characteristics of the array requires considering mutual inductance interactions between all cells in the array. We also discuss efficient numerical schemes for including these induced fields in dynamic simulation of Josephson arrays.