Hopping conduction in quasi-one-dimensional disordered compounds

Using a percolation construction we evaluate the temperature dependence of the phonon-assisted dc hopping conductivity of a model appropriate to a class of anisotropic quasi-one-dimensional conductors in which the electronic states in the vicinity of the Fermi level are localized because of intrinsic and or extrinsic static disorder. We find temperature dependences of the general form $\ln \left[\frac{\sigma \mathrm{}\left(T\right)\mathrm{}}{{\sigma }_0}\right]=-{\left[\frac{T_0\mathrm{}\left(m\right)\mathrm{}}{T}\right]}^{\frac{1}{m}}$ where $m$ is weakly temperature dependent and has the value 4 for asymptotically low temperatures, $T\to 0$ K. With increasing temperature the interchain hopping distances become smaller and $m$ decreases gradually. In a model in which the two transverse directions are equivalent, $m$ decreases to 2.91 when all allowed interchain hops are to the nearest chain only. The percolation channel is three-dimensional. For a model in which the two transverse directions are inequivalent, the percolation channel becomes two-dimensional at high temperatures when all interchain hops along the more difficult direction become more difficult than the critical percolation hop. In this case $m$ decreases to 2.70. With further increase in temperature the percolation construction breaks down in both cases. The observed conductivity of NMP-TCNQ (N-methylphenazinium tetracyanoquinodimethane) is found to be in good agreement with our results.