AbstractThe major hindrances of implementing graphene in two-dimensional (2D) electronics are both mechanical (the tendency to crumble and form ripples) and electrical (the lack of a band gap). Moreover, the inevitable structural defects in graphene have a profound influence on its physical and chemical properties. Here, we propose a family of 2D egg-tray graphenes constructed by arranging pentagon and heptagon defects in the graphene lattice based on a careful analysis of the topological distribution of minima, maxima, and saddle points. First-principles calculations show that the egg-tray graphenes are dynamically stable, and their energies, which depend on the concentration of pentagons and heptagons, are the lowest among carbon allotropes. These 2D carbon allotropes exhibit a large variation in their electronic properties, ranging from semimetallic to semiconducting, including some allotropes that have Dirac cones in their band structures. Furthermore, some egg-tray graphenes are predicted to have negative Poisson’s ratios. The adsorption of Li atoms on the egg-tray graphenes is considerably stronger than the adsorption on perfect graphene, therefore they may absorb Li more effectively than graphene, which is important for improving the performance of rechargeable Li batteries.