We have modeled flux quanta propagation in two-dimensional square arrays of small Josephson junctions when the motion is hampered by the presence of an effective barrier due to the superconducting loops. The energy barriers have been estimated simulating the effect of thermal fluctuations and evaluating the barrier via the Arrhenius factor. The results have been compared with a much simpler semianalytic method, showing that the method is able to give an acceptable estimate. The strength of the fluxon-(anti)fluxon interaction as a function of the loop inductance and the distance between the excitations has been also evaluated. It is reported that the presence of a finite inductance substantially affects the interaction potential, and the contributions due to mutual inductances are found to further change the behavior of the interaction.

• Received 31 July 2006

DOI:https://doi.org/10.1103/PhysRevB.75.054510