| The non-mediocre linear crossover of topological semimetals at the Fermi level can produce unique topological surface states,which are expected to be widely used in topological quantum computing in the future.Therefore,the research of topological semi-metallic materials has become a hot topic in recent years.Traditional topological semi-metallic materials are usually composed of heavy elements with high strength spin-orbit coupling(SOC).These heavy elements are often expensive and environmentally unfriendly,which is extremely detrimental to the practical application of materials.In the periodic table of elements,C is a typical light and environmentally friendly element with high natural content and abundant isomerization due to its extra-nuclear four-electron polyariety.In this paper,based on the bottom-up nano-assembly method,two new types of topological nodal semimetals were designed and obtained using two-dimensional carbon materials and nanotubes as the basic elements.The main research contents and results are as follows:(1)Using 2D-palgraphyne as the primitive element,3D-palgraphyne,a trivia stable carbon allotrope with Cmcm symmetry,was assembled by vertical stacking.In terms of bonding characteristics,the structure is formed by two types of carbon atoms,with three coordination and four coordination characteristics respectively,and the composition ratio is 1:2.Based on the calculations of total energy,phonon dispersion spectrum,elastic constants and first-principles molecular dynamics,the results show that the 3D-palgraphyne designed in this paper has good thermdnamic,kinetic,mechanical and thermal stability(up to 3000 K).The study of electronic structure shows that the band of 3D-palgraphyne has three pairs of linear crossover around the Fermi level,forming a typical Dirac state.The nodes form a continuous distribution of node lines in the whole Brillouin region:there are two pairs of quasi-parallel node lines in the k_x=0 plane that traverses the whole Brillouin region;In addition,there are two pairs of"dragonfly-like"joint chains on either side of the plane.The3D-palgraphyne topological properties are also investigated by using the tight bound approximation method.The results show that the linear crossings near the nodes on plane(100)are symmetrically protected and show the characteristics of energy band inversion.The projection of the nodal lines formed by them on plane(110)produces non-mediocre surface states of the tympanic membrane.In addition,we find that3D-palgraphyne exhibits the dispersion characteristics of the second type of Dirac state in some directions by calculating the energy band of different k directions with the node as the center.(2)Taking carbon(3,3)nanotubes as the basic unit,the three-dimensional nanotube bundle with the same bonding and symmetry characteristics as3D-palgraphyne was formed by combining and assembling along the radial direction,which was called 3D-(3,3)NT.Although its energy stability is less than that of3D-palgraphyne,it has good kinetic,mechanical and thermal(1000 K)stability.From the electron band structure,3D-(3,3)NT forms two linear dispersive Dirac states near the Fermi level.The nodes are also continuously distributed in the BZ.In the upper space of the BZ,one node curve appears on plane(010)and two parallel surfaces of the BZ.On plane(100),one node line runs through the whole plane and intersects with the other three nodal lines.These nodal lines appear symmetrically in the whole BZ,and the knots on the(100)surface are protected by the M_x mirror.Its topological properties are verified by the tympanic surface states on(110)surfaces.First-principles calculations combined with bottom-up assembly expanded the approach of TSM research,and provided a reference for future related research. |
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