▎ 摘　　要

Introducing a periodic array of holes, i.e., an antidot lattice, in a graphene sheet has been suggested as a route towards the tantalizing objective of "opening the gap" in this otherwise zero-gap semiconductor. Combining density-functional and mean-field Hubbard tight-binding methods, we study the effect of spin polarization on graphene antidot lattices (GALs). Focusing on GALs with extended zigzag edges, we systematically investigate the geometry dependence of spin polarization, electronic structure, and band gaps. A scaling law for the band gap is established, demonstrating marked deviations from that of circular holes without spin polarization. Furthermore, we estimate the robustness of the magnetic ordering against raised temperature and doping and, finally, consider how the optical properties are modified by spin polarization. Our results demonstrate that large, stable band gaps are expected for a range of geometries.