Theory of Nondegenerate Two‐Dimensional Electrons Interacting with Phonons in Quantizing Magnetic Fields

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Abstract
Under transverse magnetic fields the two‐dimensional electron energy spectrum transforms into a set of essentially discrete Landau levels. Taking into account the non‐parabolicity of the electron energy dispersion a quantum kinetic equation for the case of inelastic scattering by phonons is obtained. This equation is valid over a wide temperature range and at arbitrary ratios between the non‐equidistance of the Landau levels (which is connected with both the non‐parabolicity and the renormalization of the spectrum due to electron‐phonon interaction) and their widths. The shape of the cyclotron resonance peak is considered in the deformation potential approximation and also in the case of scattering by phonons whose frequency is determined by their two‐dimensional wave vector. In the latter case from the shape of the peak it is possible to obtain the phonon dispersion law.