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.