Rigid-Atom Electron-Phonon Coupling in the Tight-Binding Approximation.I

The intraband electron-phonon coupling, calculated in the tight-binding approximation, is derived from an effective deformation potential. This coupling agrees with expressions obtained by previous authors. The potential reduces to the Bardeen-Shockley deformation potential and to the Longuet-Higgins-Salem result in the long-wavelength and short-wavelength limits, respectively. The phonon-induced $d-d$ coupling alone is shown to account for the order of magnitude of the superconducting transition temperature in transition metals. The McMillan procedure for the computation of the superconductive coupling is analyzed in the case when the Fermi level falls close to a pronounced Van Hove singularity in the electron density of states. In this case the behavior of the density of states $n$ may dominate the behavior of the product $\mathrm{nV}$, where $V$ is the electron-electron effective interaction.