Phonon anomalies in strongly coupled superconductors

We discuss the connection between phonon anomalies and high superconducting temperature T_c in transition metals and their carbides, based on strong-coupling theory. Using the previously developed model theory for the lattice dynamics of these materials, we investigate the dependence on the phonon frequencies ω of the electron-phonon coupling constant λ, which essentially determines T_c. We find that the variation of the moment 〈 ω² 〉 caused by the anomalies is not enough to explain the variation of λ. This result is interpreted by assuming that the electron-phonon matrix elements which enter for λ are determined not only by a p-d contact term but also rather strongly by d-d overlap interaction.