Phonon softening in sodium with a stepwise electron distribution

The absorption of light by a metal disturbs the electron distribution around the Fermi surface. Here, we calculate the phonon dispersion relations of free-electron-like metal, bcc sodium, with a stepwise electron distribution function by using a model potential. The step can behave as a pseudo-Fermi surface, which produces singularities at specific wave numbers in the response function. The singularity gives rise to long-range oscillations in the interatomic potential and results in phonon softening along the Gamma -N direction. The effect of the smearing in the step function is also discussed.