Electronic shell and supershell structure in graphene flakes

TL;DR

This paper investigates the electronic shell and supershell structures in graphene flakes using a tight-binding model, revealing edge-dependent effects and resonance phenomena influenced by flake geometry and external potentials.

Contribution

It provides a detailed analysis of shell structures in graphene flakes, highlighting the impact of edge types and flake size, and discusses the effects of external gating on electronic states.

Findings

Valence electrons in triangular flakes exhibit shell and supershell structures.

Edge type (armchair vs zigzag) influences the shell structure and selection rules.

External gates induce resonances but do not create true bound states in graphene.

Abstract

We use a simple tight-binding (TB) model to study electronic properties of free graphene flakes. Valence electrons of triangular graphene flakes show a shell and supershell structure which follows an analytical expression derived from the solution of the wave equation for triangular cavity. However, the solution has different selection rules for triangles with armchair and zigzag edges, and roughly 40000 atoms are needed to see clearly the first supershell oscillation. In the case of spherical flakes, the edge states of the zigzag regions dominate the shell structure which is thus sensitive to the flake diameter and center. A potential well that is made with external gates cannot have true bound states in graphene due to the zero energy band gap. However, it can cause strong resonances in the conduction band.