Screening effects in the electron-optical-phonon interaction

We show that recently reported [Alexandrov and Schrieffer, Phys. Rev. B 56, 13 731 (1997)] unusual hardening of optical phonons renormalized by the el ectron-phonon interaction is due to the neglect of screening effects. When the electron-ion interaction is properly screened, optical phonons soften i n three dimensions. It is important that for short-wavelength optical phono ns screening is static, while for long-wavelength optical phonons screening is dynamic. In two-dimensional and one-dimensional cases due to crossing o f the nonperturbed optical mode with gapless plasmons, the spectrum of reno rmalized optical phonon-plasmon mode shows split momentum dependence.