  Motivated by the state of the art method for fabricating high density
periodic nanoscale defects in graphene, the structural, mechanical and
electronic properties of defect-patterned graphene nanomeshes including diverse
morphologies of adatoms and holes are investigated by means of first-principles
calculations within density functional theory. It is found that various
patterns of adatom groups yield metallic or semimetallic, even semiconducting
behavior and specific patterns can be in a magnetic state. Even though the
patterns of single adatoms dramatically alter the electronic structure of
graphene, adatom groups of specific symmetry can maintain the Dirac fermion
behavior. Nanoholes forming nanomesh are also investigated. Depending on the
interplay between the repeat periodicity and the geometry of the hole, the
nanomesh can be in different states ranging from metallic to semiconducting
including semimetallic state with the bands crossing linearly at the Fermi
level. We showed that forming periodically repeating superstructures in
graphene matrix can develop a promising technique to engineer nanomaterials
with desired electronic and magnetic properties.
