Electron and Phonon States Localized Near the Graphene Boundary

We perform analytical and numerical analysis of the electronic and phonon spectrum evolution of graphene during formation of a boundary with a “zigzag” chirality. It is determined, that the excited gap wave has a relativistic dispersion near the Fermi level that propagates along the boundary and decays with distance from it. Both properties and formation of the wave is considered. It is shown that the wave propagation occurs only along the atoms of the sub-lattice, which contains atoms with bonds broken during the boundary formation. The gap wave forms narrow resonance peaks in the local density of states of the sublattice atoms. It is shown, that the boundary formation on a graphene layer with this chirality similarly affects the phonon modes polarized normal to the layer, forming narrow maxima with frequencies nearing that of the quasiflexural phonons with the quasiwave vector at the K-point of the first Brillouin zone. This way, the formation of the “zigzag”-boundary increases both the number of charge carriers as well as the number of phonons with a large group velocity that can cause a large contribution to the electron-phonon interactions.