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

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.