Power law Kohn anomaly in undoped graphene induced by Coulomb interactions

Abstract

Phonon dispersions generically display non-analytic 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.

Some sections enlarged, new plot added

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• Symmetries and selection rules in the measurement of the phonon spectrum of graphene and related materials
• Spectroscopic investigations of phonons in epitaxial graphene
• Can freestanding Xene monolayers behave as excitonic insulators?
• Kohn anomaly of optical zone boundary phonons in uniaxial strained graphene: role of the electronic band structure