Semimetallic carbon honeycombs: new three-dimensional graphene allotropes with Dirac cones

Classic two-dimensional (2D) graphene possesses outstanding properties due to Dirac cone structures. When scaling up to three-dimensional (3D) structures, their high porosity and large surface-area-to-volume ratio made them have more promising engineering perspectives. However, the currently synthesized and density-functional-theory-predicted 3D graphene structures, termed as carbon honeycombs (CHCs), are metallic. Herein, we propose new families of stable semimetallic CHC structures, which have lower energies than the previous experimentally reported structure and they would be realized experimentally. Results from density functional theory (DFT) and tight binding (TB) model showed that multiple Dirac cones with massless Dirac Fermions are present in both pristine and strained CHCs. Dirac cones in pristine CHCs originated from interactions between sp²-hybridized carbon atoms along the zigzag direction (denoted as C, i = α, β,…), while strain-induced direction-dependent Dirac cones primarily stemmed from interactions (i) between the two C atoms bonded to a selected sp³-hybridized carbon atom or (ii) between C and C (α carbon atoms at the armchair direction) atoms. The largest Fermi velocity achieved is 1.204 × 10⁶ m s^-1, which is approximately 44.7% larger than that of graphene. These results open up a new direction in carbon-based 3D porous materials and these findings provide significant insights on numerous applications, ranging from nanoelectronics and nanomechanics to gas and liquid separations.