Quantum and classical-limit longitudinal magnetoresistance for anisotropic energy surfaces

A theory developed earlier is analyzed in the strong-field quantum as well as the weak-field classical limit for the longitudinal magnetoresistance for an anisotropic model of a multivalley semiconductor band structure. The simple analytical expressions so obtained show a change in the power law of the magnetoresistance as a function of magnetic field from the classical limit (quadratic behavior) to the quantum limit (linear behavior), in agreement with the experimental observations. The anisotropic effect which is quite important in the classical limit becomes negligible in the quantum limit.