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Dynamical simulations of fractional giant Shapiro steps

We have numerically simulated 2D arrays of resistively shunted Josephson junctions in the presence of commensurate magnetic fields and alternating and direct currents. Fractional giant Shapiro steps appear in the simulated current-voltage characteristics at values determined by the external magnetic field, in agreement with recent experimental measurements. We summarize previous results that confirm the model of vortex motion previously proposed by Benz, et al. , and present further results at low frequencies that indicate the possibility of subharmonic fractional steps.

Fractional giant Shapiro steps in 2D Josephson arrays

Radio-frequency signals were applied to 1000 by 1000 arrays of SNS Josephson junctions and giant Shapiro steps were observed at voltages 1000 times that expected for a single junction, Vn= nNhv/2e, where N=1000 is the number of junctions in the direction of applied current. For certain perpendicular magnetic fields the field-induced vortices are strongly commensurate with the array and are arranged in superlattices with qxq unit cells. In the presence of these strongly commensurate fields novel fractional giant steps were observed at voltages, Vn =n(N/q)hv/2e, directly related to q. The locking of the motion of the vortex superlattice with the applied rf current is used to explain these novel steps. The possibility of subharmonic fractional steps and preliminary measurements on disordered arrays is discussed.