Emergent Chern-Simons excitations due to electron--phonon interaction

TL;DR

This paper investigates how electron-phonon interactions in Dirac fermion systems can induce Chern-Simons excitations, affecting phonon properties and Hall conductivity, revealing new topological phenomena.

Contribution

It demonstrates the emergence of Chern-Simons excitations in phonon spectra due to fermion spectrum gaps caused by electron-phonon coupling.

Findings

Chern-Simons excitations appear in phonon spectrum

Observable effects on phonon dispersion and spectral density

Alteration of Hall conductivity due to these excitations

Abstract

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.