The oscillatory structure of the magnetophonon effect. I. Transverse configuration

The theory of the transverse magnetophonon effect in weakly coupled ( alpha <<1) polar semiconductors is developed from a perturbation expansion of the Kubo formula for conductivity to include Landau level damping. The general oscillatory structure of the resistivity is shown to depend on omega c and omega 0 , the cyclotron and optic phonon frequencies, as rho osc approximately Sigma r=1 infinity r -1 exp (-2 pi r gamma )cos(2 pi r omega 0 / omega c ) where gamma is a complicated function of the parameters of the phonon and impurity induced damping processes. For impurity broadening 2 pi gamma is proportional to omega 0 / omega c and of the order of unity, in agreement with experimental observations on GaAs.