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

We have considered the phonon-induced superconductivity and the charge-density 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 equations of motion. This procedure allows one to discuss both instabilities starting directly from the electron–phonon Hamiltonian. In contradistinction 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.