Visualizing the influence of point defects on the electronic band structure of graphene

The supercell approach enables us to treat the electronic structure of defective crystals, but the calculated energy bands are too complicated to understand or compare with angle-resolved photoemission spectra because of inevitable zone folding. We discuss how to visualize supercell band structures more effectively by incorporating unfolded spectral weights and orbital decompositions into them. We then apply these ideas to gain a better understanding of the band structure of graphene containing various types of point defects, including nitrogen impurity, hydrogen adsorbate, vacancy defects and the Stone-Wales defect.