We explore the mechanical and electronic response of sp2-based two-dimensional materials under in-plane compression employing first principles density functional theory-based calculations. Taking two carbon-based graphynes (α-graphyne and γ-graphyne) as example systems, we show that the structures of both two-dimensional materials are susceptible to out-of-plane buckling, which emerges for modest in-plane biaxial compression (1.5-2%). Out-of-plane buckling is found to be more energetically stable than in-plane scaling/distortion and significantly lowers the in-plane stiffness of both graphenes. The buckling also gives rise to in-plane auxetic behaviour in both two-dimensional materials. Under compression, the induced in-plane distortions and out-of-plane buckling also lead to modulations of the electronic band gap. Our work highlights the possibility of using in-plane compression to induce out-of-plane buckling in, otherwise planar, sp2-based two-dimensional materials (e.g. graphynes, graphdiynes). We suggest that controllable compression-induced buckling in planar two-dimensional materials (as opposed to two-dimensional materials, which are buckled due to sp3 hybridization) could provide a route to a new 'buckletronics' approach for tuning the mechanical and electronic properties of sp2-based systems. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.
Keywords: buckling; graphynes; in-plane compression; sp2 carbon-based materials; straintronics; two-dimensional materials.