Giant Shapiro Steps in Josephson Arrays: Analytical Results

Abstract

We study two-dimensional frustrated Josephson arrays driven by a combined DC plus AC current. We propose {\it ansatz} solutions that are a generalization of the solutions obtained in the DC case by Marino and Halsey (PRB {\bf 50}, 6289 (1994)). Using these solutions we derive expressions for the Shapiro step widths for $f=1/2$ and $f=1/3$ for the first few winding numbers. We show that the qualitative difference in the behaviors of the fractional and integer steps is related to the relative size of the vertical supercurrent with respect to the normal current.