Semimetallic two-dimensional defective graphene networks with periodic 4-8 defect lines

We present theoretical simulations of the electronic properties of graphene-like two-dimensional (2D) carbon networks with a periodic arrangement of defect lines formed by alternating four- and eight-membered rings. These networks can be seen as arrays of armchair-edged nanoribbons (AGNRs), which are covalently connected at the edges. Using a combination of density functional theory and a simple tight binding model, we show that the electronic properties of these networks can be understood to arise from the family behaviour of the constituting AGNRs, plus a rigid shift due to an 'inter-ribbon' coupling across the defect lines. As a result, we find one class of zero-band-gap semiconducting 2D networks, and two classes of semimetallic networks with quasi-linear band close to the Fermi energy. The formation of closed-ring electron- and hole-like Fermi surfaces due to hybridization across the defect lines offers interesting perspectives of using such defective 2D networks for transport applications or the realization of carbon-based nodal line semimetals.