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.
@article{arxiv.0710.0661,
title = {Self-consistent theory of phonon renormalization and electron-phonon coupling near a 2D Kohn singularity},
author = {O. V. Dolgov and O. K. Andersen and I. I. Mazin},
journal= {arXiv preprint arXiv:0710.0661},
year = {2009}
}