Electromagnetic microwaves in metal films with electron-phonon interaction and a dc magnetic field

A quantum-mechanical treatment of electromagnetic microwaves is performed for a metal film. The directions of the exterior ac and dc fields are taken to be arbitrary and boundary conditions for the electrons are assumed to be specular. The relation between the current and the electromagnetic field becomes nonlocal both in ordinary and Fourier space. An expression for the electron self-energy is introduced, which includes electron-phonon interaction and an effective relaxation time. The theory is applied to cyclotron phase resonance in potassium. It is suggested that the experimental peak structure in the transmission spectrum can perhaps be obtained by assuming a finite Debye temperature and specular reflections of the electrons at the boundary surfaces. A sharp peak entirely caused by the finite electron-phonon interaction is also discussed.