Universal rule on chirality-dependent bandgaps in graphene antidot lattices

Graphene with periodically patterned antidots has attracted intense research attention as it represents a facile route to open a bandgap for graphene electronics. However, not all graphene antidot lattices (GALs) can open a bandgap and a guiding rule is missing. Here, through systematic first-principles calculations, it is found that bandgaps in triangular GALs are surprisingly well defined by a chirality vector R = n a₁ + ma ₂ connecting two neighboring antidots, where a₁ and a ₂ are the basis vectors of graphene. The bandgap opens in the GALs with (n-m)mod3 = 0 but remains closed in those with (n-m)mod3 = ±1, reminiscent of the gap-chirality rule in carbon nanotubes. Remarkably, the gap value in GALs allows ample modulation by adjusting the length of chirality vectors, shape and size of the antidots. The gap-chirality relation in GALs stems from the chirality-dependent atomic structures of GALs as revealed by a super-atom model as well as Clar sextet analyses. This chirality-dependent bandgap is further shown to be a generic behavior in any parallelogram GAL and thus serves as an essential stepping stone for experimenters to realize graphene devices by antidot engineering. Graphene with periodically patterned antidots represents a facile route to open a bandgap for graphene electronics. It's found that bandgaps in graphene antidot lattices are well defined by a chirality vector R = na₁+ma₂. The bandgap opens when (n-m)mod3 is 0 but remains to be closed when (n-m)mod3 is ±1, reminiscent of the gap-chirality rule in carbon nanotubes.