High-Frequency Cyclotron Resonance in Lead and the Electron-Phonon Interaction

The frequency and temperature dependences of the electron-phonon interaction have been investigated in lead by the Azbel'-Kaner cyclotron-resonance technique. The experiments have been performed in the unusual millimeter and submillimeter microwave band from 70 to 500 GHz, corresponding to the wavelength 4 to 0.6 mm. In this frequency band the photon energy value, $\hslash \omega \le 2$ meV, is near the typical phonon energy in lead. The experiments were performed in the temperature range from 1.5 up to 6°K. The effective mass $m^{*}$ and relaxation time $\tau$, measured on two different types of orbits, are frequency and temperature dependent. These dependences are directly related to the electron-phonon interaction. For both orbits $m^{*}$ is found to increase as the temperature squared and the frequency squared. The maximum relative increases are $\frac{m^{*}\left(5.4\mathrm{}{}_{}{}^{\circ }{}_{}{}^{}K\right)}{m^{*}\left(0\mathrm{}{}_{}{}^{\circ }{}_{}{}^{}K\right)}=1.03\mathrm{}$ and $\frac{m^{*}\left(457\mathrm{} \mathrm{GHz}\right)}{m^{*}\left(0\mathrm{} \mathrm{GHz}\right)}=1.008\mathrm{}$. The relaxation frequency ${\tau }^{-1\mathrm{}}$ dependence varies as the cube of both the temperature and the frequency. The theoretical dependences on $T$ and $\omega$ are thus well confirmed, but the order of magnitude of the frequency effects is smaller than predicted.