Nonlocal screening, electron-phonon coupling, and phonon renormalization in metals.

A method for calculating the phonon self-energy in metals arising from the coupling between phonons and electrons near the Fermi surface is developed. The essence of this scheme is the separation of the inter- and intraband parts of the electron polarizability. The intraband contribution provides extra screenings and is closely related to the electron-phonon coupling and phonon softening in metals. Applications of this scheme to phonons in MgB2 give excellent results when compared with experiments and previous theoretical work. In addition, both electron and hole dopings are found to reduce the renormalization effect of the E(2g) phonon mode, which indicates a weakened electron-phonon coupling in the doped systems.