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

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