Enhancement of self-energy effects of phonons with finite wave vectors due to Fermi-surface nesting

The changes in phonon self-energy due to superconductivity are investigated for all wave vectors in the Brillouin zone, for two types of gap-function symmetry (s or d wave). We also study the phonon self-energy as a function of frequency, and for various electron concentrations. We adopt a simple tight-binding model that includes the important feature of a nested Fermi surface at half-filling. The changes in phonon self-energy arise from electron-phonon coupling. However, we make no assumption regarding the mechanism giving rise to superconductivity. We present possible signatures of an s- or d-wave gap function observable through inelastic-neutron-scattering experiments. Observation of any of these features in the high-${\mathit{T}}_{\mathit{c}}$ oxides would assist greatly in clarifying the gap function and Fermi-surface topology in these compounds.