Hopping conductivity in granular disordered systems

We study the temperature dependence of conductivity for high-resistivity granular disordered systems in terms of the critical-path method. It is shown that the low-field conductivity $\mathrm{exp}(\ensuremath{-}\frac{A}{{T}^{\ensuremath{\alpha}}})$ with $\ensuremath{\alpha}=\frac{1}{2}$ is obeyed over large temperature ranges with possible crossovers to $\ensuremath{\alpha}=\frac{1}{4}$ at low temperatures and to $\ensuremath{\alpha}>\frac{1}{2}$ at high temperatures. The temperatures at which the crossovers occur depend on the distribution of grain sizes. Comparisons are made with experiments and with other theoretical approaches.

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