Electronic structure of triangular, hexagonal and round graphene flakes near the Fermi level

TL;DR

This study investigates the electronic shell structure of various graphene quantum dots near the Fermi level, revealing edge-dependent states, the presence of ghost states in armchair triangles, and the influence of edge roughness and shape on electronic properties.

Contribution

It provides a detailed analysis of how edge geometry and shape affect the electronic states near the Fermi level in graphene flakes, highlighting the existence of ghost states and edge states.

Findings

Triangular flakes exhibit shell structure similar to free massless particles.

Ghost states appear in armchair-edged triangles but not in zigzag-edged ones.

Edge roughness has minimal effect on triangular flakes but significantly impacts others.

Abstract

The electronic shell structure of triangular, hexagonal and round graphene quantum dots (flakes) near the Fermi level has been studied using a tight-binding method. The results show that close to the Fermi level the shell structure of a triangular flake is that of free massless particles, and that triangles with an armchair edge show an additional sequence of levels ("ghost states"). These levels result from the graphene band structure and the plane wave solution of the wave equation, and they are absent for triangles with an zigzag edge. All zigzag triangles exhibit a prominent edge state at the Fermi level, and few low-energy conduction electron states occur both in triangular and hexagonal flakes due to symmetry reasons. Armchair triangles can be used as building blocks for other types of flakes that support the ghost states. Edge roughness has only a small effect on the level structure of the triangular flakes, but the effect is considerably enhanced in the other types of flakes. In round flakes, the states near the Fermi level depend strongly on the flake radius, and they are always localized on the zigzag parts of the edge.