Electronic Structure of Graphene with a Topological Line Defect

Using the first-principle total-energy procedure within the framework of density functional theory, we study the electronic structure of graphene with a topological line defect that is comprised of a pair of fused pentagons and an octagon. We find that introduction of the topological line defect effectively terminates the sp(2) network of graphene leading the flat dispersion band around Gamma point. A detailed investigation of the wave function of this flat-band state reveals its edge-state nature, which is particular to graphene nanoribbons with zigzag edges. Our tight-binding molecular dynamics simulation also reveals that the topological line defect is spontaneously formed from defects in the graphene sheet when held at a temperature of 1000 K.