Galvanomagnetic Effects in Impurity Band Conductions

Abstract

Previous theories of impurity bands in a magnetic field by the authors are extended to give a full account of the galvanomagnetic transport coefficients for the system so far introduced. The formulas for three basic components of the conductivity tensor σ _{x x} , σ _{x y} and σ _{z z} derived here are such that (1) single-site scatterings are taken into account in the one-particle and two particle Green functions all the way self-consistently, (2) they are applicable both to the intrinsic band and the impurity band simultaneously, and (3) they are applicable to any magnetic field strength. One characteristic point clarified is a reduction of the high-field Hall conductivity σ _{x y} in the impurity band region, reflecting a localized nature of the impurity band electrons. This fact is demonstrated by performing an integration involving the Fermistatistics in the expressions of the conductivities and comparing the temperature dependence of σ _{x y} with that of σ _{x x} . This provides a clear-cut theoretical confirmation that the high-field galvanomagnetic effects is InSb reported by Miyazawa (J. Phys. Soc. Japan 26 (1969),700) is in fact originated in the proposed impurity band conduction.