Accurate DC conductivity for hopping conduction within the continuous time random walk approach
The continuous time random walk approach for hopping conduction in disordered systems is modified to obtain accurate DC conductivity values over a wide range of hopping site densities. The modification involves eliminating a small fraction of particularly isolated hopping sites from the determination of the waiting-time distribution for hopping. The elimination of these sites does not correspond to a pure truncation in the transition rate spectrum, bur rather a truncation only in the distribution of contributing near-neighbor hopping distances. For a cutoff distance corresponding to the percolation radius r(p), the DC conductivity is within about 1 order of magnitude of percolation-based models and simulation results over a moderate range of hopping site densities. For a slightly larger cutoff distance of 1.15r(p), the DC conductivity is in excellent agreement with the percolation-based theory over a wide range of hopping densities. The introduction of the near-neighbor cutoff does not influence the high-frequency conductivity, where the full CTRW provides an excellent description of the conductivity. Hence, the present simple modification permits an accurate and full interrogation of the frequency-dependent conductivity within a single conceptual framework.