Structural Investigation of the Graphene TriangularNanostructure Edges and Energy Band Calculation

In this paper, we have used the Tight Binding model for the triangular graphene nanostructure, and by calculating the eigenenergy at the zigzag and armchair edges, and compared with graphene lattice energy spectra, we were able to predict the energy gap in this structure. By applying the Tight Binding Hamiltonian matrices for the unit cell and the first neighbors in the graphene lattice, we obtain the energy eigenvalues. We changed the problem conditions for the edges and observed that the zigzag edge has an electronic band with a zero-gap similar to a complete graphene lattice. But, the presence of the armchair edge has caused the formation of an energy gap. Eventually, we compared the results with experimental examples. The presence of an energy gap in the triangular nanostructure of graphene can be related to the edge of the armchair. Furthermore, the presence of active radicals and functional groups on the edge of the armchair reduces the energy gap in the nanostructure, which gives semiconductor properties to this structure.