Hopping conduction in granular metals

We modify some previous transport theories which consider only the nearest-neighbor hopping in granular metals, and compare the modified theory with the experiment of Abeles et al. In particular, we carry out a critical path analysis, and show that, with practical material parameters, the modified theory gives a value of T₀( x) in better agreement with the experiment, for the temperature-dependent conductivity σ∝ exp [-(T ₀(x)/T) ⁿ] with x=metal volume fraction and n= {1}/{2}. We have also done a resistor network simulation, and shown that the temperature range over which the exponent n= {1}/{2} is rather wide and compare reasonably with the experiment of Abeles et al.