Electronic structure of vacancy resonant states in graphene: a critical review of the single vacancy case

TL;DR

This paper critically reviews the electronic structure of vacancy-induced resonant states in graphene, focusing on zero energy modes and effects of finite vacancy concentrations within the tight-binding framework.

Contribution

It provides a detailed analysis of vacancy resonant states in graphene, clarifying the nature of zero energy modes and effects of vacancy concentration using tight-binding models.

Findings

Zero energy modes have ambiguous nature in vacancy states.

Finite vacancy concentrations influence the electronic structure.

Single vacancy states exhibit specific resonant behaviors.

Abstract

The resonant behaviour of vacancy states in graphene is well-known but some ambiguities remain concerning in particular the nature of the so-called zero energy modes. Other points are not completely elucidated in the case of low but finite vacancy concentration. In this article we concentrate on the case of vacancies described within the usual tight-binding approximation. More precisely we discuss the case of a single vacancy or of a finite number of vacancies in a finite or infinite system.