Phonon-induced contributions to superconductivity in the presence of charge-density waves

We discuss the influence of charge-density wave (CDW) order on the electron-phonon vertex and the Cooper-pair susceptibility. These quantities are investigated for different values of occupation numbers, phonon momenta and frequencies, as well as for different directions and commensurabilities of the CDW scattering vector. For the half-filled band, the onset of a CDW state results in a considerable enhancement of the electron-phonon interaction, especially when the phonon momentum is close to the scattering vector. Our results suggest that for imperfect nesting different parts of the Fermi surface contribute to a CDW and el-wave superconducting state. This feature is of particular importance for the coexistence of both phases.