Tubene: An Exotic Two-Dimensional Carbon Allotrope with Abundant Topological Quantum States

Searching for various topological quantum states near the Fermi level is a hot topic in the field of condensed matter physics. On the basis of first-principles calculations, we predict a new two-dimensional (2D) carbon allotrope assembled by (6,0) carbon nanotubes, termed Tubene. Our results show that Tubene has superb dynamical and thermal stability; in energy, it is even more stable than several synthesized 2D carbon allotropes. The analysis of the electronic properties reveals that it is an intrinsic topological semimetal with two open nodal lines across the whole first Brillouin zone, which are protected by the Mz mirror symmetry. Remarkably, multiple quantum states can be induced by modest strains, including nodal line states and different isolated nodal point states (e.g., quadratic Weyl state, linear type-II Weyl state, and linear triple degenerate state). In the low-energy band of these nodal points, strong dispersion anisotropy is detected; in particular, along a special k-direction, a kind of intriguing critical dispersion is identified for the first time, which consists of a quadratic conductive band and a valence flat band. These findings not only enrich the family of carbon allotropes but also highlight a nanotube-based assembly strategy for designing new 2D topological materials with various desirable quantum states.