Geometrical and electronic structures of graphene under different vacancy density and configuration

We calculated the geometrical and electronic structures of graphene with different vacancy densities and configurations. Vacancy was varied in graphene from mono- to tri-vacancy and configured to zigzag and armchair lattice directions. While di-vacancy in graphene led to a gap in the electronic structure, mono- and tri-vacancies shifted the Fermi level below the valence band maximum irrespective of vacancy configurations. Under the same density of vacancies, di-vacancy to zigzag direction had lower formation energy than defects along armchair direction. Meanwhile, tri-vacancy to zigzag lattice direction led to higher formation energy than defects to armchair direction.