Antidot-dependent bandgap and Clar sextets in graphene antidot lattices

By using first-principles calculations, the bandgap of two types of graphene antidot lattices (GALs) with triangular lattice, anthrancene-removed GALs and phenanthrene-removed GALs, have been studied. One third of either GALs are semiconductors as lattice parameter varies, while the lattice parameters corresponding to semiconductors are different in the two GALs, indicating the bandgap opening of GALs depends on the antidot configuration as well as lattice parameter. The bandgap opening or not is interpreted with Clarʹs aromatic sextet theory. A nonzero bandgap appears in phenanthrene-removed GALs, only when the number of Clar sextets exceeds one third of the total number of hexagons in the unit cell. However, due to a long zigzag edge existing in anthrancene-removed GALs, the bandgap can be open without meeting the condition. Our results suggest that the antidot configuration is a non negligible factor on the bandgap of graphene antidot lattices.