Effective-medium method for hopping transport in a magnetic field

An effective-medium theory for studying the influence of a magnetic field on hopping transport has been developed. It permits both the magnetoconductivity and the Hall effect to be studied in the nearest-neighbor-hopping (NNH) and in the variable-range-hopping (VRH) regime. The method has been applied to the de and ac Hall effect in three-dimensional systems. For NNH the static Hall mobility proves to be exponentially small in the critical hopping length. This fact results in a change of the sign of the Hall mobility of intermediate frequencies. For VRH the de Hall mobility exhibits a powerlike dependence on temperature. Owing to this fact the Hall mobility is nearly independent of frequency for small frequencies.