Probing the Electron-Phonon Interaction in Potassium by Far-Infrared Cyclotron Resonance

Abstract

To probe the electron-phonon interaction in potassium, Azbel'-Kaner cyclotron resonance has been observed at four frequencies in the far infrared (29.69, 32.12, 45.407, and 58.25 ${\mathrm{cm}}^{\ensuremath{-}1}$). The experiments were performed on a novel reflection cavity spectrometer with balanced homodyne detection driven by a c.w. far-infrared laser. Signals are seen for $\mathrm{E}\ensuremath{\parallel}\mathrm{H}$ and $\mathrm{E}\ensuremath{\perp}\mathrm{H}$ at 29.69 and 32.12 ${\mathrm{cm}}^{\ensuremath{-}1}$, but only for $\mathrm{E}\ensuremath{\perp}\mathrm{H}$ at 45.407 and 58.25 ${\mathrm{cm}}^{\ensuremath{-}1}$. Two effects distinguish cyclotron resonance in potassium in the infrared from that observed at microwaves. First, since the resonant electron does not escape the skin depth before the infrared field changes phase, the resonances suffer from retardation effects and are no longer amenable to the usual Azbel'-Kaner or Chambers theory of cyclotron resonance. Second, there is a strong enhancement of the electron-phonon relaxation rate due to the large density of phonon states available to scatter the excitations when the laser frequency is near the Debye frequency, $\ensuremath{\approx}75$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The line-shape analysis, used to extract the electron-phonon coupling parameter $\ensuremath{\lambda}$, does not reproduce all of the observed features. In particular, it does not reproduce absorption features on the high-field side of the subharmonic resonance which are shown to be related to the cyclotron waves that propagate across the magnetic field in the bulk. Nevertheless, by focusing attention on the breadth and position of the leading edge of the resonance, we can extract an electron-phonon $\ensuremath{\lambda}$. $\ensuremath{\lambda}$ is found to be 0.11\ifmmode\pm\else\textpm\fi{}0.02 and agrees with that determined by the temperature dependence of the phonon-limited dc resistivity.