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

Topological metals with protected band-crossing points have been attracting great interest. Here we report novel topological band features in a family of metal diboride materials. Using firstprinciples calculations, we show that these materials are metallic, and close to Fermi level, there appears coexistence of one pair of nodal rings and one pair of triply-degenerate nodal points (TNPs). The nodal ring here is distinct from the previously studied ones in that its formation requires four entangled bands, not just two as in previous cases, hence it is termed as a four-band nodal ring (FNR). Remarkably, we show that FNR features Dirac-cone-like surface states, in contrast to the usual drumhead surface states for two-band nodal rings. Due to the presence of inversion symmetry, the TNP here is also different from those discussed previously in inversion-asymmetric systems. Especially, when spin-orbit coupling is included, the TNP here transforms into a novel Dirac point that is close to the borderline between the type-I and type-II Dirac point categories. We discuss their respective symmetry protections, and construct effective models for their characterization. The large linear energy range (> 2 eV) in these materials should facilitate the experimental detection of the signatures of these nontrivial band crossings.

We study a versatile structurally favorable periodic sp 2 -bonded carbon atomic planar sheet with C 4v symmetry by means of the first-principles calculations. This carbon allotrope is composed of carbon octagons and squares with two bond lengths and is thus dubbed as octagraphene. It is a semimetal with the Fermi surface consisting of one hole and one electron pocket, whose low-energy physics can be well described by a tight-binding model of π-electrons. Its Young's modulus, breaking strength and Poisson's ratio are obtained to be 306 N/m, 34.4 N/m and 0.13, respectively, which are close to those of graphene. The novel sawtooth and armchair carbon nanotubes as well as unconventional fullerenes can also be constructed from octagraphene. It is found that the Ti-absorbed octagraphene can be allowed for hydrogen storage with capacity around 7.76 wt%.

By means of the first-principles calculations combined with the tight-binding approximation, the strain-induced semiconductor-semimetal transition in graphdiyne is discovered. It is shown that the band gap of graphdiyne increases from 0.47 eV to 1.39 eV with increasing the biaxial tensile strain, while the band gap decreases from 0.47 eV to nearly zero with increasing the uniaxial tensile strain, and Dirac cone-like electronic structures are observed. The uniaxial strain-induced changes of the electronic structures of graphdiyne come from the breaking of geometrical symmetry that lifts the degeneracy of energy bands. The properties of graphdiyne under strains are disclosed different remarkably from that of graphene. Carbon, one of the most common chemical elements in Nature, has a lot of allotropes, plenteous properties and numerous potential applications. Besides the wellknown graphite, graphene 1 , and diamond, many other novel carbon allotropes, such as T-carbon 2 , M-carbon 3 , graphyne 4,5 , graphdiyne 6 , octgraphene 7 , etc., are proposed and studied. Owing to its unique electronic 8 , mechanical and thermal properties, graphene stimulated considerable interest in itself and other two-dimensional (2D) materials 9-12 . Graphene's brothers, graphyne and graphdiyne, are also intriguing 2D carbon materials. In particular, both building blocks and cut-outs were already obtained experimentally 6,13-17 . It is known that graphene is a zero-gap semimetal, while graphdiyne is a semiconductor with a direct band gap. In addition, graphdiyne has the high-temperature stability and shows mechanical properties similar to graphene 18 , which is considered to be a potential material for nanoelectronics. The electronic modulation of graphdiyne 19-21 is thus of great interest.As graphene has no energy gap, which poses difficulties for wide applications in microelectronic devices, plenty of researches were devoted to open a band gap in graphene. One method, among others, is to invoke strains 22-28 , which is also found effective in modulating electronic properties of graphdiyne and other 2D materials such as BN sheet 29,30 . In this work, a systematic first-principles density-functional theory (DFT) study on the strain-induced changes of electronic structures in graphdiyne was performed. In the absence of a strain graphdiyne is known as a semiconductor with a direct band gap. In the presence of strains, we found that the band gap of graphdiyne increases with increasing the biaxial tensile strains, but the band gap decreases with increasing a uniaxial tensile strain either along the armchair or zigzag direction. The electronic properties around the Fermi surface are dominated by 2p z orbitals, and the Dirac cone-like electronic structures can be ob-

We propose a new topological quantum state of matter-the two-dimensional (2D) Weyl half semimetal (WHS), which features 2D Weyl points at Fermi level belonging to a single spin channel, such that the low-energy electrons are described by fully spin-polarized 2D Weyl fermions. We predict its realization in the ground state of monolayer PtCl3. We show that the material is a half metal with an in-plane magnetization, and its Fermi surface consists of a pair of fully spin-polarized Weyl points protected by a mirror symmetry, which are robust against spin-orbit coupling. Remarkably, we show that the WHS state is a critical state at the topological phase transition between two quantum anomalous Hall insulator phases with opposite Chern numbers, such that a switching between quantum anomalous Hall states can be readily achieved by rotating the magnetization direction. Our findings demonstrate that WHS offers new opportunity to control the chiral edge channels, which will be useful for designing new topological electronic devices.

Frustrated magnets hold the promise of material realizations of exotic phases of quantum matter, but direct comparisons of unbiased model calculations with experimental measurements remain very challenging. Here we design and implement a protocol of employing many-body computation methodologies for accurate model calculations-of both equilibrium and dynamical properties-for a frustrated rare-earth magnet TmMgGaO 4 (TMGO), which explains the corresponding experimental findings. Our results confirm TMGO is an ideal realization of triangular-lattice Ising model with an intrinsic transverse field. The magnetic order of TMGO is predicted to melt through two successive Kosterlitz-Thouless (KT) phase transitions, with a floating KT phase in between. The dynamical spectra calculated suggest remnant images of a vanishing magnetic stripe order that represent vortex-antivortex pairs, resembling rotons in a superfluid helium film. TMGO therefore constitutes a rare quantum magnet for realizing KT physics, and we further propose experimental detection of its intriguing properties.