Edge-dependent selection rules in magic triangular graphene flakes

Abstract

The electronic shell and supershell structure of triangular graphene quantum dots has been studied using density functional and tight-binding methods. The density functional calculations demonstrate that the electronic structure close to the Fermi energy is correctly described with a simple tight-binding model, where only the ${p}_{z}$ orbitals perpendicular to the graphene layer are included. The results show that (i) both at the bottom and at the top of the ${p}_{z}$ band, a supershell structure similar to that of free electrons confined in a triangular cavity is seen, (ii) close to the Fermi level, the shell structure is that of free massless particles, (iii) triangles with armchair edges show an additional sequence of levels (``ghost states'') absent for triangles with zigzag edges while the latter exhibit edge states, and (iv) the observed shell structure is rather insensitive to the edge roughness.