Phonon Effects on the Cyclotron Resonance for a Many-body System: a Generalized Quantum Langevin Equation Approach

We have recently developed a new approach to the derivation of quantum transport results for an interacting many-body system of electrons, impurities and phonons. Now, using a similar philosophy, the cyclotron resonance lineshape (CRLS) of an electron-phonon many-body system is studied by the generalized quantum Langevin equation approach, in which the memory function is obtained directly by solving the Heisenberg equation of the motion for the fluctuating density of relative electrons. Frequency dependent line shift and line width results, for the case of interacting electrons in the RPA approximation, are derived in a very simple way. A systematic study of the temperature and magnetic field dependences of the CRLS of a two dimensional electron-phonon system is performed. Two resonance peaks, due to the acoustic phonon absorption and emission process, are found in the vicinity of the cyclotron resonance frequency.