Tight-Binding Approximation Calculation on the Electronic Structure of Graphene and Graphene Nanoribbons

Abstract

The electronic structure expression of graphene was derived using tight-binding approxi-mation method. According to periodic boundary conditions in width direction of graphene nanorib-bons wave vector, the electronic structure analytical expression of armchair graphene nanoribbons was deduced, and the energy band curve were given. The conditions of graphene nanoribbons being metal or semiconductor were obtained. The results show that when nanoribbons width meetsL=3na/2, the energy gap is zero and armchair graphene nanoribbons behave as the metallic. With the increase of the nanoribbons width, the energy gap of semiconducting nanoribbons decreases. The electronic properties of graphene nanoribbons are closely related to their geometry. The graphene nanoribbons can be modulated into metal or semiconductor with different band gap by controlling their width.