Electron-screening effects on the self-trapping of polarons

In a polar semiconductor with a number of electrons or holes in the conduction or valence band, the interactions of an external charge with the longitudinal optical phonon are screened by the electron/hole density. Consequently the self-energy depends on the density. We show that, for any value of the Fröhlich electron-phonon coupling constant α, an electronic density n^* can be found such that for density n≳n^* the Lee polaron theory for the intermediate coupling (not self-trapped polarons) gives self-energies lower than those of the strong coupling (self-trapped polarons). This is due to the static and dynamical screening introduced by the plasmon field on the electron-phonon interaction. This result is confirmed by applying the path-integral technique to the problem and calculating both the self-energy and the renormalized mass. It is found that the density n^* depends on α and η (the ratio of the high frequency dielectric constant to the static one). We note that typical charge carrier densities in high T_c superconductors are larger than n^* for a wide range of value of α. This indicates that no self-trapped polarons might have a role in high T_c superconductors. © 1996 The American Physical Society.