Quantum-limit cyclotron resonance linewidth due to an electron-phonon interaction

Abstract

The cyclotron resonance line shape is dependent upon the current relaxation rate $\ensuremath{\Gamma}(k)$. We have numerically determined $\ensuremath{\Gamma}(k)$ and hence the cyclotron resonance linewidth $\ensuremath{\gamma}$ in the quantum limit for a nondegenerate semiconductor using a previously derived formula [J. Phys. Chem. Solids 41, 735 (1980)]. The electrons are assumed to interact with acoustic phonons via a deformation potential. For high temperatures we have found that the dependence of the linewidth $\ensuremath{\gamma}$ and peak absorption ${P}^{max}$ on the temperature and the resonance frequency ${\ensuremath{\omega}}_{0}$ is given approximately by $\ensuremath{\gamma}\ensuremath{\propto}{T}^{\frac{1}{2}}{\ensuremath{\omega}}_{0}$, ${P}^{max}\ensuremath{\propto}{T}^{\frac{\ensuremath{-}1}{2}}{\ensuremath{\omega}}_{0}^{\ensuremath{-}1}$, whereas for low temperatures $\ensuremath{\gamma}\ensuremath{\propto}{T}^{6.5}{\ensuremath{\omega}}_{0}^{\ensuremath{-}2}$, ${P}^{max}\ensuremath{\propto}{T}^{\ensuremath{-}6.5}{\ensuremath{\omega}}_{0}^{2}$. The line shape is found to be almost Lorentzian. We have compared our numerical results for $\ensuremath{\Gamma}(k)$ with the various approximations which are commonly employed.