Linear response theory revisited. IV. Applications

The one-body linear response expressions (diagonal and nondiagonal) for the dc electrical conductivity, obtained in a previous paper, are applied to specific situations. In the case of ‘‘no collisional current’’ we evaluate the relaxation times which enter an expression (diagonal) for the longitudinal magnetoconductivity; in the case of ‘‘collisional current’’ another expression (diagonal) for the transverse magnetoconductivity is evaluated. The calculations are carried out in the framework of electron–phonon interaction in crystalline materials; various kinds of phonons are considered. The formula for ‘‘collisional current’’ is also used for an analytic evaluation of the phonon assisted hopping conductivity in crystalline and amorphous materials. The results are in harmony with those of the literature or are new. Further, the nondiagonal expression leads to a result for the oscillatory Hall effect, which, in contrast with previous results, is independent of the interaction (e.g., interaction with impurities).