We address the problem of Dirac fermions interacting with longitudinal phonons. A gap in the spectrum of fermions leads to the emergence of the Chern--Simons excitations in the spectrum of phonons. We study the effect of those excitations on observable quantities: the phonon dispersion, the phonon spectral density, and the Hall conductivity.
Cite
@article{arxiv.1505.04194,
title = {Emergent Chern-Simons excitations due to electron--phonon interaction},
author = {Andreas Sinner and Klaus Ziegler},
journal= {arXiv preprint arXiv:1505.04194},
year = {2016}
}