CALCULATION OF GIANT FRACTIONAL SHAPIRO STEPS IN JOSEPHSON-JUNCTION ARRAYS

We calculate the rsponse of an N×N array of resistively shunted Josephson junctions to an imposed current I=Idc+Iacsin(2t). In a transverse dc magnetic field of p/q==f flux quanta per plaquette of area, we find fractional giant Shapiro steps in the time-averaged voltage n=1,2,3,..., in agreement with the measurements of Benz et al. At f=1/5, 2/5, and 1/3, we find additional fractional steps at 4e). A generalization of the model of Benz et al. accounts for both the fractional giant steps at p/q and the anomalous half-integer steps. © 1990 The American Physical Society.