The effect of edges and shapes on band gap energy in graphene quantum dots

We perform a theoretical study of the structural properties of graphene quantum dots (GQD) by means of atomistic tight-binding theory. The calculations consist of the single-particle spectra and band gaps as a function of the sizes. The computations highlight that the resulting calculations of band gap are mainly sensitive with the shapes and type of edges of GQD. The band gaps from tight-binding model are quite consistent with the other theoretical data. The same shapes of GQD can have different band gaps if they have different edge types. The lower band gap is observed on rectangular GQD compared with parallelogram GQD.