Electronic properties and quasi-zero-energy states of graphene quantum dots

In this paper, research has been carried out on the electronic properties of nanostructured graphene. We focus our attention trapped states proposed systems such as spherical and toroidal graphene quantum dots (GQDs). Using a continuum model, by solving Dirac-Weyl equation, applying periodic boundary conditions two types, i.e., either with zigzag edges only or both armchair edges, we obtain analytical results for energy levels yielding self-similar bands located subsequently one after another scale. Only dot (owing to lack curvature) distribution electron density is like Bohr atomic orbitals. However, although quasi-zero-energy band exists dots, no present dot. This causes formation pseudogap between hole because absence at center, in case an ordinary atom. Conversely, confinement charge-carrier observed geometries GQDs.