Three-dimensional graphdiyne as a topological nodal-line semimetal

We study the electronic band structure of three-dimensional ABC-stacked (rhombohedral) graphdiyne, which is a new planar carbon allotrope recently fabricated. Using the first-principles calculation, we show that the system is a nodal-line semimetal, in which the conduction band and valence band cross at a closed ring in the momentum space. We derive the minimum tight-binding model and the low-energy effective Hamiltonian in a $4\times 4$ matrix form. The nodal line is protected by a non-trivial winding number, and it ensures the existence of the topological surface state in a finite-thickness slab. The Fermi surface of the doped system exhibits a peculiar, self-intersecting hourglass structure, which is quite different from the torus or pipe shape in the previously proposed nodal semimetals. Despite its simple configuration, three-dimensional graphdiyne offers unique electronic properties distinct from any other carbon allotropes.