Structural, elastic, and electronic properties of topological semimetal WC-type MX family by first-principles calculation

Recently, the non-centrosymmetric WC-type materials(i.e., MoP, ZrTe, TaN, etc) have attracted extensive interest due to the discovery of their topological properties.By means of the first-principles calculations, here we have investigated the structural, thermodynamic, elastic, and electronic properties of the WC-type MX compounds(TiS, TiSe, TiTe, ZrS, ZrSe,ZrTe, HfS, HfSe, and HfTe).Among these nine compounds, five of them(TiS, ZrS, ZrSe0.9, ZrTe, and Hf0.92 Se) have been experimentally synthesized to crystallize in the WC-type structure and other four members have never been reported.Our calculations demonstrated that they are all structurally, thermodynamically, and dynamically stable, indicating that all of them should be possibly synthesized.We have also derived their elastic constants of single crystalline and their bulk and shear moduli in terms of the R.Hill approximations.Furthermore, in similarity to ZrTe, all these compounds have been theoretically derived to be topological semimetals.Whereas TiS is unique because of the coexistence of the Dirac nodal lines(DNLs) and sixfold degenerate nodal points(sixfold DNPs), the other eight members are revealed to exhibit coexisted Weyl nodes(WPs) and triply degenerate nodal points(TDNPs).Their electronic and topological properties have been further discussed.

General principles to high-throughput constructing two-dimensional carbon allotropes

We propose general principles to construct two-dimensional(2D)single-atom-thick carbon allotropes.They can be viewed as the generalization of patterning Stone–Walse defects(SWDs)by manipulating bond rotation and of patterning inverse SWDs by adding(or removing)carbon pairs on the pristine graphene,respectively.With these principles,numerous 2D allotropes of carbon can be systematically constructed.Using 20 constructed 2D allotropes as prototypical and benchmark examples,besides nicely reproducing all well-known ones,such as pentaheptites,T-graphene,OPGs,etc,we still discover 13 new allotropes.Their structural,thermodynamic,dynamical,and electronic properties are calculated by means of first-principles calculations.All these allotropes are metastable in energy compared with that of graphene and,except for OPG-A and C3-10-H allotropes,the other phonon spectra of 18 selected allotropes are dynamically stable.In particular,the proposed C3-11 allotrope is energetically favorable than graphene when the temperature is increased up to 1043 K according to the derived free energies.The electronic band structures demonstrate that(i)the C3-8 allotrope is a semiconductor with an indirect DFT band gap of 1.04 e V,(ii)another unusual allotrope is C3-12 which exhibits a highly flat band just crossing the Fermi level,(iii)four allotropes are Dirac semimetals with the appearance of Dirac cones at the Fermi level in the lattices without hexagonal symmetry,and(vi)without the spin–orbit coupling(SOC)effect,the hexagonal C3-11 allotrope exhibits two Dirac cones at K and K points in its Brillouin zone in similarity with graphene.