Hopping in quasi-one-dimensional disordered solids: Beyond the nearest-neighbor approximation

The theory of hopping transport in quasi-one-dimensional disordered organic solids with Gaussian distribution of localized state energies is generalized to account for distant-neighbor transitions. The former theories predicted a temperature dependence of the resistivity of the form In p proportional to C(sigma/kT)(2), where C is a constant (C approximate to 1) and sigma is the disorder parameter. It is shown that the onset of second-nearest neighbor hopping leads to a decrease of C with decreasing temperature to the limiting value C = 3/4. At lower temperatures, where the hopping range extends beyond second-nearest neighbors, C is expected to decrease further. The analytical results are in fair agreement with the results of Monte Carlo simulation for one-dimensional variable-range hopping.