Power-law Kohn anomaly in undoped graphene induced by Coulomb interactions

Abstract

Phonon dispersions generically display nonanalytic points, known as Kohn anomalies, due to electron-phonon interactions. We analyze this phenomenon for a zone-boundary phonon in undoped graphene. When electron-electron interactions with coupling constant \beta are taken into account, one observes behavior demonstrating that the electrons are in a critical phase: the phonon dispersion and lifetime develop power-law behavior with \beta-dependent exponents. The observation of this signature would allow experimental access to the critical properties of the electron state, and would provide a measure of its proximity to an excitonic insulating phase.