Collective Cooper-pair transport in the insulating state of Josephson-junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are nonmonotonic functions of the magnetic field. We propose that formation of the dynamic Coulomb barrier and its size scaling are consequences of the mutual Josephson phase synchronization across the system. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.