Localized electron states near the armchair edge of graphene

Abstract

It is known that zigzag graphene edge is able to support edge states: there is a non-dispersive single-electron band localized near the zigzag edge. However, it is generally believed that no edge states exist near the armchair edge. In this paper we re-examine this notion. It is demonstrated that while, indeed, the pristine armchair edge does not support any localized states, they do appear if the edge is subjected to suitable modifications (e.g. chemical functionalization). We explicitly present two types of the edge modification which support the localized states. Unlike zigzag edge states, which have zero energy and show no dispersion, properties of the armchair localized states depend sensitively on the type of edge modification. Under suitable conditions they demonstrate pronounced dispersion. While the zigzag edge state wavefunction decays monotonously when we move away from the edge, the armchair edge state wavefunction shows non-monotonous decay. Such states may be observed in scanning tunneling spectroscopy experimentally.

11 pages, 11 figures. Typos were corrected, figures 5,6,11 were updated. The main result of paper is unchanged

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• Kane-Mele Hubbard model on a zigzag ribbon: stability of the topological edge states and quantum phase transitions
• Resonant electron scattering by graphene antidot
• Electrostatic forces above graphene nanoribbons and edges interpreted as partly hydrogen-free
• Resonance Absorption of Terahertz Radiation in Nanoperforated Graphene