Hybridization bond states and band structure of graphene: a simple approach

Abstract

Abstract This article reviews the basic theoretical aspects of graphene in order to contribute to making teaching easier and more understandable for those who still cannot understand it in an abstract way. This work presents the basic aspects of sp2 hybridization concepts from a quantum approach, which consists in obtaining the states for the sigma bonds from carbon atoms orientation close to another carbon atom that is our reference point in the crystal lattice. Furthermore, we calculate the band structure of graphene by using the tight-binding model, which can give us a good approximation to the energy levels as a function of the wave vector. This is for students interested in solid-state topic and it is approached in a simple and understandable way step by step to finally obtain the bands structure of the primitive cell of graphene monolayer. Additionally, we calculate the high symmetry points of the first Brillouin zone and the analysis around K points to obtain the well-known Dirac cones. The intention of this work is to show that this topic can be less abstract than it seems.