Theory of magnetophonon resonance in quantum wells

In a polar semiconductor mixed optic phonon-magnetoplasmon vibrations can be trapped within a quantum well. Such localized vibrations effectively interact with the confined electrons of the quantum well. We demonstrate that these excitations can be responsible for the magnetophonon resonance oscillation of the conductivity of quantum wells, i.e., phonon-induced resonant transitions of electrons between the Landau levels. The frequency of the mixed vibrations is shifted, due to the screening effects, towards the frequency of transverse optic vibrations ${\omega }_t.$ This can explain the observed shift of the magnetophonon resonance in quantum wells. We give theoretical considerations to determine a (rather narrow) interval of electron concentrations where a two-dimensional magnetophonon resonance is observable.