Electronic properties investigation of Graphene and Boron Nitride nanoribbons utilizing the Tight-Binding model

The electronic properties of Carbon based nanomaterials have been attracted the attention of the scientific community for decades. The structural details of these systems are of fundamental importance to describing their properties. With the objective of offering a fundamental review that allows entry into research areas related to nanoscience, this work is dedicated to investigating the electronic properties of one-dimensional physical systems in a systematic and pedagogical way. We use a simple Tight – Binding model to obtain the band structure of these systems and describe their electronic behavior. At first, we describe the methodology used, demonstrating its simplicity for understanding introductory concepts in nanoscience. Then, we determine the energy band of a linear chain of atoms, considering only one site per unit cell. In order to offer an extrapolation of this system, we apply our model to Graphene and Boron Nitride nanoribbons, which can be interpreted as the interpenetration of linear chains, displaying N sites per unit cell. Finally, despite the simplicity of the proposed model, we demonstrate that the presented calculations show consistency with more robust formalisms, such as the DFT.

Keywords:
Electronic properties; Tight-Binding model; Graphene nanoribbons; Boron Nitride nanoribbons