Power law Kohn anomaly in undoped graphene induced by Coulomb interactions

TL;DR

This paper investigates how Coulomb interactions induce a power law Kohn anomaly in undoped graphene, revealing critical electron behavior through phonon dispersion and lifetime modifications.

Contribution

It demonstrates that electron-electron interactions cause power law behavior in phonon properties, indicating a critical phase in undoped graphene.

Findings

Power law phonon dispersion and lifetime with interaction-dependent exponents

Signature of critical electron phase in phonon behavior

Potential experimental measure of proximity to excitonic insulator

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.