Theory of cyclotron resonance halfwidth for electrons scattered by impurities and phonons

Abstract

A general theory of the cyclotron resonance halfwidth for electrons scattered by impurities and phonons is developed on the basis of the proper connected diagram expansion of the current-correlation-function formula for the dynamic conductivity. The theory is applied to the cases of Ge samples at extremely high magnetic fields and different temperatures. The usual form of Matthiessen's rule Γ = Γ 1 + Γ 2 + …, where Γ and Γ j are the total and component energy-dependent resonance widths, is valid only if the component widths Γ j computed separately for each cause of scattering depend linearly on the densities of scatterers. The resonance width Γ I due to the charged impurities at very low electron densities ( $ ̃ 10 12 cm −3) and at very low temperatures is known to vary in proportion to the square-root of the impurity density. Large deviations from the Matthiessen's rule occur in such a case. The theory is in good quantitative agreement with currently available experimental data. In order to test the generalized form of Matthiessen's rule, however, the high-field resonance experiments around 15 K is desirable where both phonon and impurity scatterings contribute in a comparable manner.