Edge-dependent selection rules in magic triangular graphene flakes

TL;DR

This study investigates the electronic shell and supershell structures in triangular graphene quantum dots, revealing edge-dependent selection rules and the influence of edge types on electronic states near the Fermi level.

Contribution

It demonstrates that a simple tight-binding model accurately describes the electronic structure near the Fermi energy and uncovers edge-dependent selection rules in triangular graphene flakes.

Findings

Supershell structure resembles that of free electrons in a triangular cavity.

Near the Fermi level, electrons behave as massless particles.

Armchair edges show additional 'ghost' states, zigzag edges exhibit edge states.

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.