Electronic structure of worm-eaten graphene

We theoretically study the electronic structure of graphenes having several kinds of imperfections such as atomic vacancies and heteroatom replacements. We consider 12 different configurations of vacancies and 39 different geometries of heteroatom replacements in order to approximately take into account the random conformations of imperfections. To systematically provide a perspective understanding of the defect π and σ states caused by atomistic voids and/or vacancies and heteroatom replacements, we have carried out a tight-binding (TB) calculation. We study the orbital hybridization to clarify the origin and formation of π and σ defect states arising from such imperfections. We also discuss the electronic structure around the Fermi level through the TB band calculation.