The recurrent relations for the electronic band structure of the multilayer graphene

Abstract

The structure of the electronic energy bands for stacked multilayer graphene is developed using the tight-binding approximation (TBA). The spectra of the Dirac electrons are investigated in vicinity of the Brillouin zone minima. The electron energy dependence on quasi-momentum is established for an arbitrary number of the graphene layers for multilayer graphene having even number of layers N  = 2 n , ( n  = 2, 3, 4, …) with the Bernal stacking ABAB … AB; or for odd number of layers N  = 2 n  + 1, ( n  = 1, 2, 3, …) with stacking ABAB … A. It is shown that four non-degenerate energy branches of the electronic energy spectrum are present for any number of layers. Degeneracy is considered of graphene-like energy branches with linear dispersion law. Dependences of such branches number and their degeneracy are found on number of layers. The recurrent relations are obtained for the electronic band structure of the stacked ABA…, ABC… and AAA… multilayer graphene. The flat electronic bands are obtained for ABC-stacked multilayer graphene near the K -point at the Fermi level. Such an approach may be useful in the study of multivarious aspects of graphene's physics and nanotechnologies. Also paper gives new hints for deeper studies of graphite intercalation compounds.