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.
@article{arxiv.1012.3162,
title = {Frequency splitting of intervalley phonons in graphene},
author = {K. Ziegler and E. Kogan},
journal= {arXiv preprint arXiv:1012.3162},
year = {2011}
}