Some aspects of impurity conduction

To study diffusion and localization of electrons in impurity bands, the self-consistent current relaxation theory is applied to Wegner's local gauge-invariant model for random hopping transport. The approach covers both the conducting and the insulating phase for arbitrary dimensionality $d$ within a single framework. Explicit results for the mobility, the static polarizability, and the frequency-dependent conductivity are given for $d=2\mathrm{}$ and 3. For $d=2\mathrm{}$, an abrupt transition from a state of strong localization to a weakly localized quasimetallic phase is found. Scaling laws for the conductivity near the mobility edge are worked out and the role of the upper critical dimensionality $d=4\mathrm{}$ is discussed.