FULL CAPACITANCE MATRIX EFFECTS IN DRIVEN JOSEPHSON-JUNCTION ARRAYS

We study the dynamic response to external currents of periodic arrays of Josephson junctions, in a resistively capacitively shunted junction model, including full capacitance-matrix effects. We define and study three different models of the capacitance matrix C-(r over right arro w,(r) over right arrow'): model A includes only mutual capacitances; m odel B includes mutual and self-capacitances, leading to exponential s creening of the electrostatic fields; model C includes a dense matrix C-(r over right arrow,(r) over right arrow') that is constructed appro ximately from superposition of an exact analytic solution for the capa citance between two disks of finite radius and thickness. In the latte r case the electrostatic fields decay algebraically. For comparison, w e have also evaluated the full capacitance matrix using the MIT FASTCA P algorithm, good for small lattices, as well as a corresponding conti nuum effective-medium analytic evaluation of a finite-voltage disk ins ide a zero-potential plane. In all cases the effective C-(r over right arrow,(r) over right arrow') decays algebraically with distance, with different powers, We have then calculated current-voltage characteris tics for dc+ac currents for all models. We find that there are giant c apacitive fractional steps in the I-V's for models B and C, strongly d ependent on the amount of screening involved. We find that these fract ional steps are quantized in units inversely proportional to the latti ce sizes and depend on the properties of C-(r over right arrow,(r) ove r right arrow'). We also show that the capacitive steps are not relate d to vortex oscillations but to localized screened phase locking of a few rows in the lattice. The possible experimental relevance of these results is also discussed. [S0163-1829(98)01426-X].