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We use a simple tight-binding (TB) model to study electronic properties offree graphene flakes. Valence electrons of triangular graphene flakes show ashell and supershell structure which follows an analytical expression derivedfrom the solution of the wave equation for triangular cavity. However, thesolution has different selection rules for triangles with armchair and zigzagedges, and roughly 40000 atoms are needed to see clearly the first supershelloscillation. In the case of spherical flakes, the edge states of the zigzagregions dominate the shell structure which is thus sensitive to the flakediameter and center. A potential well that is made with external gates cannothave true bound states in graphene due to the zero energy band gap. However, itcan cause strong resonances in the conduction band.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Electronic shell and supershell structure in graphene flakes