Relaxing the graphite lattice along critical directions: The effect of the electron-phonon coupling on the π electron band structure

We investigate the effects on the electronic structure induced by a relaxation of the graphite lattice along the direction of the phonons associated to the G and to the D peak characteristic of the Raman spectra of graphitic materials. To this aim the bond length dependence of the hopping integral β is introduced in a Hückel (tight-binding) hamiltonian, giving rise to two different β1 and β2 parameters. A Peierls-like gap opening is found for a relaxation along the D peak phonon and not for the G peak phonon. The electronic density of states is discussed and a link is shown between the electronic structure of benzene and the electronic structure of graphene at the K point in reciprocal space.