Theory of shapiro steps in Josephson-junction arrays and their topology

A simple theory of Shapiro steps in a Josephson-junction (JJ) array immersed in a magnetic field is presented. It is argued that the system can be regarded as the superposition of a JJ array in zero field and a vortex lattice generated by the magnetic field. The subsystems obey the resistively-shunted-junction equations of motion, and interference effects result in steps at 1/{ital q},2/{ital q},. . . for a filling factor {ital p}/{ital q}. The exactness of the steps is shown to result from the topological quantization of the order parameter for dissipative systems.