Zone-Boundary Phonon Induced Mini Band Gap Formation in Graphene

TL;DR

This paper theoretically demonstrates that coupling between electrons and zone-boundary phonons in graphene can induce a mini band gap at the Brillouin zone corners, highlighting a potential mechanism for band gap engineering.

Contribution

The study introduces a Fröhlich-type Hamiltonian to analyze electron-phonon interactions in graphene, revealing a phonon-induced mini band gap formation at the K and K' points.

Findings

Electron-phonon coupling induces a mini band gap in graphene.

Zone-boundary phonons of A1g symmetry are responsible for gap formation.

Lattice distortions may be enhanced by electron-electron interactions.

Abstract

We investigate the effect of electron- $\mathrm{A}_{1g}$ phonon coupling on the gapless electronic band dispersion of the pristine graphene. The electron-phonon interaction is introduced through a Kekul\'{e}-type distortion giving rise to inter-valley scattering between K and K' points in graphene. We develop a Fr\"ohlich type Hamiltonian within the continuum model in the long wave length limit. By presenting a fully theoretical analysis, we show that the interaction of charge carriers with the highest frequency zone-boundary phonon mode of $% \mathrm{A}_{1g}$-symmetry induces a mini band gap at the corners of the two-dimensional Brillouin zone of the graphene. Since electron-electron interactions favor this type of lattice distortion, it is expected to be enhanced, and thus its quantitative implications might be measurable in graphene.