Density functional study of graphene antidot lattices: Roles of geometrical relaxation and spin

Graphene sheets with regular perforations, dubbed as antidot lattices, have theoretically been predicted to have a number of interesting properties. Their recent experimental realization with lattice constants below 100 nanometers stresses the urgency of a thorough understanding of their electronic properties. In this work, we perform calculations of the band structure for various hydrogen-passivated hole geometries using both spin-polarized density functional theory (DFT) and DFT based tight-binding (DFTB) and address the importance of relaxation of the structures using either method or a combination thereof. We find from DFT that all structures investigated have band gaps ranging from 0.2 to 1.5 eV. Band gap sizes and general trends are well captured by DFTB with band gaps agreeing within about 0.2 eV even for very small structures. A combination of the two methods is found to offer a good trade-off between computational cost and accuracy. Both methods predict nondegenerate midgap states for certain antidot hole symmetries. The inclusion of spin results in a spin-splitting of these states as well as magnetic moments obeying the Lieb theorem. The local-spin texture of both magnetic and nonmagnetic symmetries is addressed.