Effects of tensile strain on the electronic structure of graphene nanomesh

Creating a graphene nanomesh, that is graphene sheet with a regular array of holes, which can also be referred to as antidot lattice, is one of the ways to open the electronic band gap in graphene. Using focused electron irradiation in a transmission electron microscope and programmed beam displacements, we prepare nanomeshes with periodicities below 10 nm and hole sizes below 3 nm. We find that the formation of the mesh is frequently accompanied by the appearance of vacancy lines, which should give rise to the mechanical strain in the system. Moreover, strain can also appear upon heating or cooling graphene sheet along with the supporting frame, or exerted externally. At the same time, the effects of strain on the electronic structure of graphene nanomeshes has not been studied. The main goal of this work is to investigate theoretically how tensile strain and vacancy lines can affect the band gap in the nanomeshes with and without hydrogen termination. Using first-principles calculations, we demonstrate that for most structures the gap (if present) monotonously decreases with strain. However, when strain gives rise to the changes in the morphology of the edges, the gap can be opened or closed, which is associated with the spatial localization of the electron wave functions at the valence band maximum and conduction band minima. The magnetic moments localized at the edge atoms of the nanopore change as well. We further discuss such a behavior in the context of the optoelectronic properties of graphene antidot lattices, along with the implications for strain engineering of the characteristics of the nanomeshes.