Structural, energetic, and electronic properties of gyroidal graphene nanostructures

Nanostructures configured as triply periodic minimal surfaces, such as gyroidal systems, possess a broad range of potential applications as energy and storage materials and can be used as elementary building blocks for complex electronics. Here, we investigate the effect of structure size and material density on a number of sp² carbon gyroid structures. We describe a general Monte Carlo method for discovering atomic structures of carbon gyroids of arbitrary size that obey the prescribed space group symmetry for gyroid surfaces. A total of 19 structures are investigated, among which we find three types of ground state structures corresponding to a given number of atomic cycles present in the asymmetric unit cell. Each type is characterized by the distribution of non-hexagonal rings: type I structures present a minimum number of non-hexagonal rings (octagons), while type II (type III) structures include square and heptagon (pentagons and octagons) in addition to hexagons. We use density functional theory to establish how electronic, topological, geometric, and energetic properties of these gyroids vary with size and density. We determine that most studied systems feature occupied and unoccupied three-dimensional Dirac hyper-cones and metallic and semi-conducting behaviors.