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

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.