Flux flow and vortex tunneling in two-dimensional arrays of small Josephson junctions

We have measured the temperature dependence and magnetic field dependence of the zero-bias resistance ((Formula presented)) as well as the current-voltage (I-V) characteristics for several two-dimensional arrays of small aluminum Josephson junctions. (Formula presented)(T) decreases with decreasing temperature, which can be described in terms of two types of vortex motion: flux, flow, and vortex tunneling. At temperatures higher than the Kosterlitz-Thouless transition temperature (T>(Formula presented)) or at a bias current greater than the current corresponding to the onset of the nonlinear I-V characteristics (I>(Formula presented)), the effective damping resistance which characterizes flux-flow motion is found to be approximately equal to the junction normal-state resistance (Formula presented). At low temperatures and at small bias current, (Formula presented) is temperature independent and remains finite down to our minimum attainable temperature. This finite resistance is found to be dependent on the array size as well as the junction parameters.