  Ideal graphene antidot lattices are predicted to show promising band gap
behavior (i.e., $E_G\simeq 500$ meV) under carefully specified conditions.
However, for the structures studied so far this behavior is critically
dependent on superlattice geometry and is not robust against experimentally
realistic disorders. Here we study a rectangular array of triangular antidots
with zigzag edge geometries and show that their band gap behavior qualitatively
differs from the standard behavior which is exhibited, e.g, by rectangular
arrays of armchair-edged triangles. In the spin unpolarized case, zigzag-edged
antidots give rise to large band gaps compared to armchair-edged antidots,
irrespective of the rules which govern the existence of gaps in armchair-edged
antidot lattices. In addition the zigzag-edged antidots appear more robust than
armchair-edged antidots in the presence of geometrical disorder. The inclusion
of spin polarization within a mean-field Hubbard approach gives rise to a large
overall magnetic moment at each antidot due to the sublattice imbalance imposed
by the triangular geometry. Half-metallic behavior arises from the formation of
spin-split dispersive states near the Fermi energy, reducing the band gaps
compared to the unpolarized case. This behavior is also found to be robust in
the presence of disorder. Our results highlight the possibilities of using
triangular perforations in graphene to open electronic band gaps in systems
with experimentally realistic levels of disorder, and furthermore, of
exploiting the strong spin dependence of the system for spintronic
applications.
