Fractional giant Shapiro steps and spatially correlated phase motion in 2D Josephson arrays

We have applied radio-frequency signals to 1000 by 1000 arrays of Josephson junctions and observed giant Shapiro steps at voltages 1000 times that expected for a single junction. When a perpendicular magnetic field is applied, fractional giant steps appear at voltages directly related to the number of flux quanta per unit cell. A phenomenological model is proposed that utilizes the spatial arrangement of the vortices in a superlattice relative to the underlying array to explain these novel steps.