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

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.

8 pages, 2 figures

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Cited by in corpus (5)

• Energy Gaps and Kohn Anomalies in Elemental Superconductors
• Quantitative reliability of Migdal-Eliashberg theory for strong electron-phonon coupling
• Breakdown of the Migdal-Eliashberg theory and a theory of lattice-fermionic superfluidity
• Strong electron-phonon interaction in multiband superconductors
• Electron-phonon interaction in the lamellar cobaltate Na${}_x$CoO${}_2$