Competition between superconductivity and charge-density waves in the electron-phonon system

We have considered the phonon-induced superconductivity and the charge-dens ity waves. In order to find the leading contributions to the corresponding Green functions we made use of the decoupling on the second stage of the eq uations of motion. This procedure allows one to discuss both instabilities starting directly from the electron-phonon Hamiltonian. In contradistinctio n to the standard BCS-type approach we have taken into account modification of the normal-state properties which occur because of the electron-phonon interaction. It has been found that these many-body effects can contribute effectively to the stabilization of the superconducting phase. (C) 1999 Els evier Science Ltd. All rights reserved.