Electron-phonon mass enhancement and lifetime at finite temperature

We reexamine the effect of the electron-phonon interaction on the electron mass enhancement and inverse lifetime as a function of temperature. We assign the values of the quasiparticle energy and inverse lifetime to the real and imaginary parts of the pole in the single-electron Green function, following Galitskii and Migdal. We find that for intermediate to strong coupling the electron mass enhancement grows monotonically with temperature and the electron inverse lifetime is almost independent of the electron-phonon coupling parameter. This result corrects the conventional wisdom that the mass enhancement has a maximum as a function of temperature, and that the inverse lifetime grows linearly with coupling constant, statements which remain true for weak coupling. In contrast, electron-impurity scattering leads to a decrease of the electron mass enhancement parameter.