The effect of local-field correction on the transport properties of crystals

Abstract

The question of local-field correction to the electrical transport is studied in more detail; namely, for the hopping limit and the band limit. In the hopping limit, if the hopping takes place between crystallographically equivalent sites, the short-range and Lorentz contributions to the dipolar potentials cancel in taking the intersite energy difference, and the electric field appearing in the hopping conductivity is just the macroscopic field. However if the hopping takes place between crystallographically inequivalent sites the short-range contributions to the dipolar potentials at the two sites do not cancel although the Lorentz contributions do. This leads to local-field-type corrections. The resulting corrections are found to be negligible at low fields but considerable at higher fields. Similar results are found for the Hall mobility of the small-polaron and AC impurity hopping conduction. In the band limit, it is shown that when the motion occurs in one band the net electric field appearing in the transport equation is just the macroscopic field unmodified by the local-field corrections.