Coexistence of Dirac nodal loops and triply degenerate nodal points in three-dimensional interpenetrated <i>α</i>-graphyne

Recently, constructing three-dimensional materials through two-dimensional materials is attracting research attention in both experiment and theory due to the properties beyond ordinary 3D materials. In this work, we propose a three-dimensional carbon allotrope by interpenetrating α-graphyne sheets with van der Waals interactions and study its structural and electronic properties by first-principles calculations and tight-binding methods. Our calculations show that the energy of this interpenetrated α-graphyne is slightly lower than that of the α-graphyne nanosheet due to the weak van der Waals interactions, and its dynamical and thermodynamical stabilities are further confirmed by first-principles calculations. Remarkably, 3D interpenetrated α-graphyne is a semimetal with both Dirac nodal loops and triply degenerate nodal points near the Fermi level and the Fermi velocities at these nodal points are very high. These properties are superior to 2D α-graphyne and ordinary 3D carbon materials. Our work not only proposes a type of 3D carbon material with multiple types of fermions for carbon-based high-speed nanoelectronic devices but also shows that interpenetrating 2D materials with large hollows is a promising method for constructing 3D materials.