Theoretical Approach to Investigate the Band Structure of Multilayers Armchair Graphene Nanoribbons (MLAGNRs)

Abstract

The electronic band structure for the stacked multilayer armchair graphene nanoribbon (MLAGNRs) is presented theoretically by using the generalized effective long-wave Hamiltonian and the tight-binding approximation. The relation between the energy gap and the number of layers in a wide range of energies around Fermi's energy level is calculated numerically. The energy of the electron depends on the momentum is investigated for an arbitrary number of layers for the armchair graphene nanoribbon having number of layers n = 1, 2 and 3 with the stacking ABC. We find, in agreement with previous calculations, that MLAGNRs are changeable from conducting to semiconducting according to the number of stacked layers and the width of the armchair graphene nanoribbons. Our results revealed the behavior of the flat electronic bands for ABC-stacked multilayer armchair graphene nanoribbon at the K-point around Fermi’s energy level. This study may be useful in various forms of graphene’s physics. Thus, it emphasized the possibility of controlling the electronic properties as required by the techniques based on these nanomaterials