Frequency splitting of intervalley phonons in graphene

TL;DR

This paper investigates how strong electron-phonon interactions in graphene can cause a splitting of intervalley phonons, leading to a phase transition that could be detected via Raman spectroscopy.

Contribution

It introduces a theoretical framework describing phonon splitting and associated phase transition in graphene due to electron-phonon coupling.

Findings

Weak coupling preserves phonon degeneracy

Strong coupling causes phonon splitting into optical and acoustic branches

Predicted Berezinskii-Kosterlitz-Thouless transition in phonon behavior

Abstract

We study the thermal distribution of intervalley phonons in a graphene sheet. These phonons have two components with the same frequency. The degeneracy of the two modes is preserved by weak electron-phonon coupling. A sufficiently strong electron-phonon coupling, however, can result in a splitting into an optical and an acoustic phonon branch, which creates a fluctuating gap in the electronic spectrum. We describe these effects by treating the phonon distribution within a saddle-point approximation. Fluctuations around the saddle point indicate a Berezinskii-Kosterlitz-Thouless transition of the acoustic branch. This transition might be observable in the polarization of Raman scattered light.