Abstract
We study hexagonal graphene quantum dots, using density functional theory, to obtain a quantitative description of the electronic properties and their size dependence, considering disk and ring geometries with both armchair and zigzag edges. We show that the electronic properties of quantum dots with armchair edges are more sensitive to structural de-tails than those with zigzag edges. As functions of the inner and outer radii, we find in the case of armchair edges that the size of the band gap follows distinct branches, while in the case of zigzag edges it changes monotonically. This behaviour is further analyzed by studying the ground state wave function and explained in terms of its localisation.