Zone-boundary phonon induced mini band gap formation in graphene

We investigate the effect of electron– A 1 g phonon coupling on the gapless electronic band dispersion of the pristine graphene. The electron–phonon interaction is introduced through a Kekulé-type distortion giving rise to inter-valley scattering between K and K ′ points in graphene. We develop a Fröhlich 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 A 1 g - symmetry induces a mini band gap at the corners of the two-dimensional Brillouin zone of the graphene in the THz region. 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.