Comment on frequency- and temperature-dependent electron-phonon renormalization effects

Abstract

The temperature ($T$) and frequency ($\omega$) shifts of the electron mass enhancement $\lambda$ and scattering rate $\frac{1}{\tau }$ are discussed for small $T$ and $\omega$. A catalogue of formulas is given for $\lambda$ and $\frac{1}{\tau }$ for quasiparticles of energy $\hslash \omega$ and also averaged over quasiparticle energies between 0 and $kT$ or $\hslash \omega$. Recent cyclotron-resonance experiments by Goy and Castaing are shown to be in fairly good agreement with the averaged theories once certain algebraic difficulties are corrected.