Half-negative Poisson’s ratio in graphene+ with intrinsic Dirac nodal loop

Summary: Carbon materials have attracted extensive attention in the past decades due to the rich configurations and outstanding properties. Numerous efforts have been dedicated to obtaining two-dimensional (2D) materials inheriting the properties of graphene. Herein, from first-principles calculations, we report a novel 2D carbon allotrope with a hybridized sp2-sp3 network, i.e., “grapheneplus (graphene+)”. Both the Dirac properties of graphene and the negative Poisson’s ratio (NPR) of penta-graphene are inherited in graphene+. The NPR behavior manifests itself along the out-of-plane direction only when it is stretched, namely, out-of-plane half-auxeticity, which is different from the already known NPR behavior. Besides, the Dirac nodes form a nodal loop that remains robust regardless of the application of uniaxial/biaxial strain and electric field. In addition, graphene+ is found to be energetically more stable than penta-graphene, which promises a potentially easier synthesis. In short, graphene+ could act as a strong competitor to graphene.