Pseudo-Fermi surface and phonon softening in sodium with a stepwise electron distribution

TL;DR

This paper investigates how a stepwise electron distribution in sodium affects phonon behavior, revealing phonon softening and potential instabilities linked to pseudo-Fermi surface effects.

Contribution

It introduces a model with a stepwise electron distribution to study phonon dispersion, highlighting the role of pseudo-Fermi surfaces in phonon softening.

Findings

Singularities at specific wavenumbers in response function

Imaginary phonon frequencies indicating instability

Long-range oscillations in interatomic potential

Abstract

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 pseudo-potential method. The step can behave as a pseudo-Fermi surface, which produces the singularities at specific wavenumbers in the response function. The singularity gives rise to long-range oscillations in the interatomic potential and results in imaginary phonon frequencies around the N point.