Experiments and model calculations on small regular Josephson networks

Niobium spheres were arranged in a regular lattice forming a 2D network of Josephson junctions. The current-voltage characteristics of this network were measured under microwave irradiation showing giant Shapiro steps. When a weak magnetic field was applied perpendicular to the sample fractional giant Shapiro steps appeared additionally, possibly caused by a collective motion of flux. All the characteristics observed experimentally can be reproduced in the frame of a network model which we developed for numerical simulations of Josephson arrays including inductive coupling of junctions with finite capacitances and thermal noise.