Doppler-shifted cyclotron resonance in thin metal films

The velocities of electrons contained in a thin slab are quantized because the component of momentum transverse to the slab faces is quantized. For a free electron gas the transverse velocity is given by |v_H| = l(/m) (π/d) where l = 1, 2, 3, …. If a magnetic field is applied normal to the slab, the wave number and frequency dependent conductivity consists of a series of resonant terms. The resonances occur at the Doppler-shifted cyclotron resonance frequencies |ω_c| = ω ± p(/m) (π/d)² where l = 1, 2, 3, …. It is shown that these resonances in the conductivity result in an absorption in pure thin films at low temperatures which is periodic in magnetic field. The semi-classical expression for the absorption is in substantial agreement with the corresponding quantum calculation, and has the virtue that it may be readily extended to non-spherical Fermi surfaces.