A Few Topological Semimetal:First Principles Studying

According to their electronic resistance,all bulk materials are divided into metals,which have a finite electron density at the Fermi energy,and insulators,which show a band gap.Insulator and metal can be further classified as topological insulator(TI)and metal,according to their topological properties.Topological insulator is similar with the normal one inside the bulk as an insulator.But on the edges or the surfaces they are significantly different,because of the existence of the conduction states on the surface of TI.Generally,the conducting states on the surfaces are protected by some special symmetries,such as Time reversal or inversion symmetry.On the edges,the electrons with different spin move in the different directions.So,not only the charge but also the spin can be used to transform informations.The topological materials may be used in the quantum calculations.In the all,topological materials is the hot topic in the field of condenser materials.According to their topological properties,they can be classified as:1.Topological insulators and Topological semimetals(TSM).Researchers firstly found the TI and then the TSM.TSM is a new state in the condenser mater,including Weyl and Dirac semimetal,and is different with the 3D TI.It is characterized by the nodes in the bulks and Fermi arcs on the surfaces.Around the nodes,the low energy physics is represented by the Weyl Himation HW=v?·k or the Dirac Himation(?)The Weyl semimetal requires either time reversion or inversion symmetry being broken.While Dirac semimetal needs to keep both time reversion and inversion symmetry.If the Weyl nodes and the Dirac nodes form a line,this material is called as Nodal-line semimetal.The above three kinds of semimetal will be studied in this thesis.Firstly,we briefly introduce the new concept of topological materials about TI and TSM and the researching method and theory.From chapter 3 to chapter 6,the topological materials studied in this thesis are detailed.In the chapter 3,the strain dependence of the electronic structures,thermoelectric and topological properties of the half-Heusler compounds ZrIrX(X=As,Sb,Bi)are investigated.At the equilibrium lattice constants,all the three compounds are trivial insulators and good thermoelectric materials with the Seebeck coefficient S and the power factor over relaxation time S2?/? as large as 1180(?V/K)and 4.1(1011Wm-1 K-2s-1),respectively.The compressive strain enhances the band gap,while the tensile strain decreases the band gap.At some specific tensile strains,the compounds become Dirac-semimetals,with the s-type band ?6 below p-type band ?8,in the cubic phase.When we compress the a(b)-axis and elongate the c-axis of the compounds,they become the type-I Weyl semimetals.For ZrIrAs.the eight Weyl-Points(WPS)locate at(±Kx,0,±Kz),(0,±Ky,±Kz).Kx=Ky=0.008?-1,Kz=0.043?-1.In the chapter 4,we studied the electronic structures and topological properties of the Hexagonal and Heusler structures NaAuTe,by using the first-principles calculations and tight-bonding analysis,.Without spin-orbit-coupling(SOC),the Hexagonal NaAuTe is a nodal-line semimetal.When SOC is included,it becomes Dirac semimetal,with two Dirac points(DP)on the Kz-axis,at(0.0,±0.2012?/c).The Heusler structure NaAuTe is a Dirac semimetal in the cubic crystal and Weyl semimetal in the tetragonal crystal structure.For the tetragonal NaAuTe,there are four pairs of WPS at(±0.021,0,±0.039)and(0,±0.021,±0.039).Such significantly different topological properties are due to their structures induced different crystal field splitting and p-d hybridizations.In the chapter 5,the topological properties of NaAuS and NaAuTe were studied by first-principles calculation,K·P and tight bonding method.It was found that their topological properties depend on the effective Spin-Orbit-Coupling(SOC).Negative SOC induces TI just like NaAuS,while positive SOC generates TSM as NaAuTe.The discovery of TSM is more challenging than that of TI,especially for the Weyl-semimetal,whose Weyl-points usually locate at some points away from the high-symmetry planes and lines.Here,we provided the general rules to design TI and TSM compounds,such as TI NaAuS and TSM NaAuTe.Since the effective SOC can be tuned by the p-d hybridization,it can be used to design new topological materials.The design scheme is:1.firstly,induce'band inversion'in the materials,such as pushing the s-typed band below the p-typed band;2.introducing the strong p-d hybridization,which changes the energy level.According to the above rules,XYZ(X=Li,Na,K;Y=Ag,Au;Z=O,S)might be the candidates that can realize TI and TSM.In the chapter 6,we studied the topologically nontrivial Weyl semimetal Os2.There are two different types:(i)the standard Weyl cones with point-like Fermi surfaces(type-?)and(ii)tilted Weyl cones that appear at the contact of electron and hole pockets(typeII).These two types of Weyl semimetals have significantly different physical properties in their thermodynamics and magnetotransport.Here we presented a compound OsC2 with both types Weyl Points(WPs)at the equilibrium volume.It has 24 type-?WPs in the Kz=±0.0241×2?/c planes around K(or K')points and 12 type-? WPs in the Kz=±0.4354×2?/c planes at projected K(K')-point,respectively.The type-? WPs are connected by the Helix-Trimer Fermi arcs.In the chapter 7,we summarized the research methods and content of this thesis.The prospect of topological materials is discussed in the chapter.The shortcoming of the thesis is also mentioned,companying with our future research to go beyond the present works.