Self-consistent theory of phonon renormalization and electron-phonon coupling near a 2D Kohn singularity

TL;DR

This paper develops a self-consistent theoretical framework for phonon renormalization and electron-phonon coupling in 2D metals, resolving divergences near Kohn singularities that occur with traditional methods.

Contribution

It introduces a self-consistent approach to accurately evaluate electron-phonon interactions near Kohn singularities in 2D metals, correcting previous divergence issues.

Findings

No divergence in coupling constant near Kohn singularity with self-consistent method

Standard expressions fail near Kohn singularity in 2D metals

Self-consistent theory provides a more accurate description of phonon behavior

Abstract

We show that the usual expression for evaluating electron-phonon coupling and the phonon linewidth in 2D metals with a cylindrical Fermi surface cannot be applied near the wave vector corresponding to the Kohn singularity. Instead, the Dyson equation for phonons has to be solved self-consistently. If a self-consistent procedure is properly followed, there is no divergency in either the coupling constant or the phonon linewidth near the offending wave vectors, in contrast to the standard expression.