Edge state in graphene ribbons: Nanometer size effect and edge shape dependence

TLDR

Graphite systems with zigzag edges host a localized edge state that produces flat bands at the Fermi level and a sharp density‑of‑states peak, whereas armchair edges lack such states. The study investigates how system size and edge shape influence the edge state in graphene ribbons using a ribbon model. The authors model graphene ribbons with varying widths and mixed zigzag‑armchair edges to analyze the edge state. They find that nanometer‑scale width and the presence of at least three zigzag sites per sequence are essential for a significant edge state, which dominates the density of states near the Fermi level even in ribbons with mixed edges.

Abstract

Finite graphite systems having a zigzag edge exhibit a special edge state. The corresponding energy bands are almost flat at the Fermi level and thereby give a sharp peak in the density of states. The charge density in the edge state is strongly localized on the zigzag edge sites. No such localized state appears in graphite systems having an armchair edge. By utilizing the graphene ribbon model, we discuss the effect of the system size and edge shape on the special edge state. By varying the width of the graphene ribbons, we find that the nanometer size effect is crucial for determining the relative importance of the edge state. We also have extended the graphene ribbon to have edges of a general shape, which is defined as a mixture of zigzag and armchair sites. Examining the relative importance of the edge state for graphene ribbons with general edges, we find that a non-negligible edge state survives even in graphene ribbons with less developed zigzag edges. We demonstrate that such an edge shape with three or four zigzag sites per sequence is sufficient to show an edge state, when the system size is on a nanometer scale. The special characteristics of the edge state play a large role in determining the density of states near the Fermi level for graphite networks on a nanometer scale.