Additional Coulomb blockade and negative differential conductance in closed two-dimensional tunnel junction arrays

We have theoretically investigated the transport properties of a two-dimensional array of small tunnel junctions having two different paths between the source and the drain electrodes. We have found that at zero temperature the Coulomb interaction between tunneling electrons in the upper and the lower branches of the array can bring about stationary configurations of electrons which completely block further influx of electrons from the source at voltages above the usual Coulomb blockade. This “additional” Coulomb gap is transformed into a negative differential conductance regime at finite temperature. We also discuss the effect of imperfection of arrays on the additional Coulomb blockade phenomena.