【作者】 张敏平；

【导师】 杨宗献；

【作者基本信息】 河南师范大学 ， 凝聚态物理， 2020， 博士

【摘要】 按照导电性质的不同,材料可分为“导体”和“绝缘体”两大类;而更进一步,根据电子态的拓扑性质的不同,“绝缘体”和“导体”还可以进行更细致的划分。拓扑绝缘体就是根据这样的新标准而划分的区别于其他普通绝缘体的一类绝缘体。拓扑绝缘体的体内与人们通常认识的绝缘体一样,是绝缘的,但是在它的边界或表面总是存在导电的边缘态,这是它有别于普通绝缘体的最独特的性质。这样的导电边缘态在保证一定对称性(比如时间反演对称性)的前提下是稳定存在的,而且不同自旋的导电电子的运动方向是相反的,所以信息的传递可以通过电子的自旋,而不像传统材料通过电荷来传递。拓扑材料有可能用于量子计算等领域,是当前凝聚态物理领域的研究热点。根据其电子态拓扑性质可以将其粗略分为两类:1.拓扑绝缘体;2.拓扑半金属。人们首先认识到的是拓扑绝缘体,而后是拓扑半金属。拓扑半金属是一类新的量子拓扑态,包含外尔半金属和狄拉克半金属,它不同于三维拓扑绝缘体(TI),其低能有效模型为Weyl费米子和Dirac费米子,费米“面”是孤立的点,投影到表面会出现费米弧。Weyl费米子的有效哈密顿量形式为HW=v(?)·(?),是两分量体系,其中k是晶体动量,σ是泡利矩阵。各个方向的费米速度(?)给出了两类不同手征(左旋或右旋)的Weyl费米子,其被看成动量空间的磁单极子。Weyl费米子要求破坏时间反演对称性(TR)或者中心反演对称。如果有这两种对称性,就得到有效哈密顿量为四分量的狄拉克方程:(?)。如果上述外尔点和狄拉克点形成连续的线,就叫节线半金属,Nodal-line Semimetal。本博士论文将研究上述三种拓扑半金属的热电和拓扑性质。在本论文中,首先简单描述了拓扑材料的概念,引入了拓扑绝缘体和拓扑半金属的概念;然后在第二章概括了拓扑半金属的研究方法和所需要的理论基础;在第三章到第六章中,详细介绍了几种拓扑半金属的具体工作。其中,在第三章,研究了ZrIrX(X=As,Sb,Bi)在各种压力下的电子结构、热电性质和拓扑性质。在平衡体积下,三种材料都是平庸半导体,且其热电性质非常好。当体积被压缩时,带隙变大。相反,当材料受到张应力时候,带隙变小。张应力继续增大时,具有s轨道特征的Γ6被推到具有p-d杂化轨道特征的Γ8之下,材料转为狄拉克半金属。在材料中进一步引入晶格畸变,压缩a-b面使a=0.98a0,同时拉伸c轴使c=1.02a0,原来立方相中绕体对角线[111]的三度旋转对称性C3消失,材料进入外尔半金属相。第四章研究了六角结构和半哈斯勒结构的NaAuTe的拓扑性质。对于六角结构,在没有考虑自旋轨道耦合(SOC)时候是节线半金属。当把SOC考虑进去以后,六角NaAuTe是狄拉克半金属,立方相的NaAuTe也是狄拉克半金属;但是它的狄拉克点分布和六角结构的明显不同,只存在于Γ点。在六个反射面(kx=±ky,ky=±kz,kz=±kx)上有外尔点形成的12条环线。这些环线在晶体的对称性从立方结构变成四方结构时,退化为4对外尔点,分布在(kx=±0.021,ky=0,kz=±0.039)and(kx=0,ky=±0.021,kz=±0.039)。第五章利用第一性原理、K.P微扰、紧束缚模型等综合手段研究了 NaAuS和NaAuTe的拓扑性质。发现NaAuS的有效SOC强度是负的,而NaAuTe的有效SOC为正,因而NaAuS是拓扑绝缘体,而NaAuTe是拓扑半金属。基于有效SOC可以调节,我们提出了改变材料拓扑性质的办法,并提出了设计拓扑材料的指导思路:1.首先实现能带翻转,即,s轨道能级在p型轨道能级之下;2.强的p-d杂化,因为p,d电子相反的SOC劈裂顺序,它们可以提供正负SOC两种类型的材料。根据上面的原则,我们提出XYZ(X=Li,Na,K;Y=Ag,Au;Z=O,S)可能实现上面的要求。第六章第一次在自然平衡条件下同一材料中发现了第一型和第二型外尔点共存的外尔半金属OsC2。发现在Kz=0.0241×2π/c平面内,绕K点有三个正外尔点,旋转60度的K’点有三个负的外尔点环绕着K’点。与Kz=0.0241×2π/c相对Kz=0镜面对称的面Kz=-0.0241×2π/c上有相反的外尔点。在K和K’的正上方,Kz=0.4354×2π/c面有第二型外尔点存在。对于第一型外尔点,我们发现它们的连接方式为“螺旋三角构型”。第七章是本博士论文的总结与展望。对本论文所用的研究方法和内容给出总结,对拓扑材料的发展方向进行展望。发现论文的研究需要更进一步的地方,同时提出今后的研究方向和目标。更多还原

【Abstract】 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=vσ·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 S2σ/τ as large as 1180(μV/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 Γ6 below p-type band Γ8,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,±0.2012π/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-Ⅰ)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-ⅠWPs in the Kz=±0.0241×2π/c planes around K(or K’)points and 12 type-Ⅱ WPs in the Kz=±0.4354×2π/c planes at projected K(K’)-point,respectively.The type-Ⅰ 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.更多还原