A structurally stable crystalline carbon allotrope is predicted by means of the first-principles calculations. This allotrope can be derived by substituting each atom in diamond with a carbon tetrahedron, and possesses the same space group Fd3m as diamond, which is thus coined as T-carbon. The calculations on geometrical, vibrational, and electronic properties reveal that T-carbon, with a considerable structural stability and a much lower density 1.50  g/cm3, is a semiconductor with a direct band gap about 3.0 eV, and has a Vickers hardness 61.1 GPa lower than diamond but comparable with cubic boron nitride. Such a form of carbon, once obtained, would have wide applications in photocatalysis, adsorption, hydrogen storage, and aerospace materials.

We theoretically study the three-dimensional topological semimetals with nodal surfaces protected by crystalline symmetries. Different from the well-known nodal-point and nodal-line semimetals, in these materials, the conduction and valence bands cross on closed nodal surfaces in the Brillouin zone. We propose different classes of nodal surfaces, both in the absence and in the presence of spinorbit coupling (SOC). In the absence of SOC, a class of nodal surfaces can be protected by spacetime inversion symmetry and sublattice symmetry and characterized by a Z2 index, while another class of nodal surfaces are guaranteed by a combination of nonsymmorphic two-fold screw-rotational symmetry and time-reversal symmetry. We show that the inclusion of SOC will destroy the former class of nodal surfaces but may preserve the latter provided that the inversion symmetry is broken. We further generalize the result to magnetically ordered systems and show that protected nodal surfaces can also exist in magnetic materials without and with SOC, given that certain magnetic group symmetry requirements are satisfied. Several concrete nodal-surface material examples are predicted via the first-principles calculations. The possibility of multi-nodal-surface materials is discussed.arXiv:1712.09773v2 [cond-mat.mes-hall]

A second-order topological insulator (SOTI) in d spatial dimensions features topologically protected gapless states at its (d − 2)-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state, it has been attracting great interest, but it remains a challenge to identify a realistic SOTI material in two dimensions (2D). Here, based on combined first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized 2D material graphdiyne as the first realistic example of a 2D SOTI, with topologically protected 0D corner states. The role of crystalline symmetry, the robustness against symmetry-breaking, and the possible experimental characterization are discussed. Our results uncover a hidden topological character of graphdiyne and promote it as a concrete material platform for exploring the intriguing physics of higher-order topological phases.Lattice structure.-GDY is a carbon allotrope with a 2D planar network structure [ Fig. 1(a)], which may be viewed as formed by inserting the diacetylenic linkage between two neighboring benzene rings in a graphene structure. The lattice is completely flat, with a single-atom arXiv:1904.09985v2 [cond-mat.mes-hall] 3 Jan 2020