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 electron-phonon interaction is due to the neglect of screening effects. When the electron-ion interaction is properly screened, optical phonons soften in three dimensions. It is important that for short-wavelength optical phonons screening is static, while for long-wavelength optical phonons screening is dynamic. In two-dimensional and one-dimensional cases due to crossing of the nonperturbed optical mode with gapless plasmons, the spectrum of renormalized optical phonon–plasmon mode shows split momentum dependence.