# Mutual inductance effects in rf driven planar Josephson junctions arrays

Research paper by G. Filatrella, A. Petraglia, G. Rotoli

Indexed on: 01 Nov '99Published on: 01 Nov '99Published in: The European Physical Journal B

#### Abstract

In this paper we investigate the behavior of moderate size two-dimensional classical arrays of Josephson junctions in presence of an external oscillating field. We have included in the model the effects due to mutual inductance terms, and we have employed an explicit set of differential equations. We have found that the discretization parameter βL - i.e. the coupling term due to the inductance of the loops - is the most important parameter to determine the height of the Shapiro steps for a given amplitude and frequency of the rf-bias. The amplitude of the Shapiro steps in the case of zero frustration as a function of the coupling term shows a remarkable minimum for intermediate values when we retain all terms of the full model with mutual inductances, while the limits for very large and very small values of βL they are the same of the single Josephson junction. For the case of frustration 1/2 the Shapiro step becomes smaller in the rigid limit (i.e., small βL as expected for the XY model, and tends to the limit value of the single junctions for the decoupled case (i.e., large βL).