Ohmic magnetoresistance for inelastic acoustic phonon scattering in semiconductors

The effect on both the longitudinal and the transverse magnetoresistance of a parabolic semiconductor with isotropic effective mass of the inelasticity of the acoustic phonons is studied in the framework of the Arora-Peterson density-matrix formalism. To exhibit clearly the effect of inelasticity, the numerical computations are done for a model where electrons are assumed to interact strongly with phonons of wave vector $q\sim \frac{1}{\lambda }$, where $\lambda$ is the radius of the cyclotron orbit. It is found that inelasticity changes the transverse magnetoresistance dramatically, while the Hall coefficient and the longitudinal magnetoresistance remain essentially unchanged.