High-Frequency Cyclotron Resonance in an Electron-Phonon Gas

The surface impedance of an isotropic electron-phonon gas in the presence of a static magnetic field and high-frequency electromagnetic wave ($\omega \sim {\omega }_D$, the Debye frequency) has been calculated. The calculation is based on a recently derived quantal transport equation, by one of the authors, which is modified to include the effects of the external magnetic field. The resultant expression for the (wave-vector- and frequency-dependent) bulk conductivity $\sigma (q,\omega )$ incorporates effects due to electron-phonon interaction (EPI). The bulk conductivity is related to the surface impedance by the standard expression for the extreme anomalous limit. The EPI effects are manifested in the surface impedance by (a) a frequency-dependent effective cyclotron mass, and (b) frequency-dependent damping (attenuation of the higher subharmonics) associated with frequency-dependent collision processes.