On the Hall effect in hopping impurity conduction

Abstract

The green function approach is used for the calculation of the AC transverse conductivity in the hopping regime of the impurity conduction. This approach enables the author to clarify what type of absorption contributes to the Hall effect. The result is that only the direct (resonant) absorption occurs. On the other hand, he finds out what approximations are involved in Holstein's early calculations. He concludes that these approximations are not achieved by the experimental circumstances, a fact which explains the discrepancy between the Holstein theory and experiments. Another problem discussed is the way of calculation of the conductivity in the hopping regime. It is explained why it is correct to calculate the induced dipole moment rather than the current.