强自旋轨道耦合体系的第一性原理研究

发布时间：2019-03-17 12:23

【摘要】：自旋轨道耦合相互作用是电子所表现出来的一种相对论效应。在2005年,Kane等人发现自旋轨道耦合相互作用可以导致拓扑绝缘体相变,自旋轨道耦合相互作用在凝聚态中显得越发的重要。自旋轨道耦合相互作用大小与原子的核电荷数的四次方成正比,所以原子序数越大自旋轨道耦合相互作用越大。因此对于第六周期以及部分第五周期的元素组成的化合物,我们需要把自旋轨道耦合相互作用考虑进来。5d过渡金属氧化物与3d、4d体系相比,它的轨道在实空间分布比较扩展,因此电子关联U相对3d、4d过渡族元素来说比较小。所以可以预期从3d到5d,体系从绝缘体变为金属。但是很多5d体系却表现出绝缘体行为,这是由于5d过渡族元素往往具有强自旋轨道耦合相互作用。在自旋轨道耦合相互作用和电子关联以及晶格的相互作用相互竞争下,5d过渡金属氧化物蕴含着丰富的物理。比如Mott绝缘体、复杂磁性、拓扑绝缘体、Weyl半金属等。对于重元素Bi、Pb、Te、Sb、Sn等来说它们的自旋轨道耦合相互作用也很强,所以很多拓扑绝缘体都包含这些重元素,例如HgTe/CdTe量子阱、Bi2Se3等。除了拓扑绝缘体,人们也发现了拓扑保护的半金属。现在拓扑半金属总共分为三类：Dirac半金属、Weyl半金属、node-line半金属。Dirac半金属和Weyl半金属中的Dirac点和Weyl点在动量空间离散分布并且数目有限。它们的表面态有特征的费米弧。Dirac半金属在打破时间反演或者空间反演对称性会转化为Weyl半金属。而node-line半金属的能带在费米面附近相交并且交点有无数个,这些交点在倒空间连成一条线。对于理想的node-line半金属来说,所有的交点都落在在同一个能量面上,那么它的表面态是一个平带。这给研究超导、分数量子霍尔效应提供了一个平台。寻找强自旋轨道耦合相互作用体系的材料并且研究这些材料所表现出的丰富的物理是十分有意义的课题。基于密度泛函理论,紧束缚模型,k·p微扰理论,我们研究几类强自旋轨道耦合的材料：我们首先系统地研究了5d过渡金属化合物NaOsO3,并且发现它是一个新型的三维Slater绝缘体。我们系统地计算了NaOsO3电子结构,并且搜索了它的磁结构,发现它的磁基态是G型反铁磁。自旋轨道耦合相互作用不能使体系打开能隙,同样电子关联也不可以使体系打开能隙。只有当体系处在G型反铁磁时,才会打开一个能隙,这就证明了NaOsO3是一个三维的Slater绝缘体。我们理论预言的磁结构随后被实验所证实。其次,我们预言了一个新型的三维Dirac半金属BaYBi(Y=Cu、Ag、Au)。这类Dirac半金属材料比较稳定,组成成分没有剧毒,给实验研究和工业应用带来很大的方便。BaCuBi和BaAgBi的电子结构相似：Bi的6p带在自旋轨道耦合相互作用以及晶体场的联合作用下,在r点穿过Ag-5s(Cu-4s)带形成反带结构,并且沿着F-A形成交点(Dirac点)。而BaAuBi的反带结构发生在Bi的6p带之间。我们也探讨了掺杂可以使得这个三维的Dirac半金属变为Weyl半金属。然后我们讨论了Weyl半金属NbP的电子结构和表面态。NbP是最近发现的非中心反演的Weyl半金属材料TaAs家族的一员。NbP在不加自旋轨道耦合时,能带在镜面对称保护下形成node-line。当考虑自旋轨道耦合相互作用以后,每条node-line会演化为一对手性相反的Weyl点。它们的表面态具有特别的蝌蚪形状。我们的理论计算结果和ARPES实验测量结果非常吻合。通过选择一条闭合的曲线并查看这条闭合曲线穿过费米面的次数,我们最终确定NbP是一个Weyl半金属。最后我们发现CsCl结构的二元化合物CaTe,在忽略自旋轨道耦合相互作用时,是一个node-line半金属。它有三条互相垂直的node-line,并且这三条node-line都在M点附近。我们研究了这个拓扑node-line半金属的表面态,发现它的表面态是一个鼓面一样的二维平带。这个给研究超导、分数量子霍尔效应提供了一个平台。而当加上自旋轨道耦合相互作用以后,这个拓扑node-line半金属就会变为Dirac半金属。它的三条node-line会打开能隙,仅仅在M-R线上保留交点。这个交点是由M-R线上的C4旋转对称性保护而稳定。如果打破C4旋转对称性,比如加上应力,那么这个三维的Dirac半金属会演变为强拓扑绝缘体。
[Abstract]:The spin-orbit coupling interaction is a relativistic effect that is exhibited by the electrons. In 2005, Kane et al. found that the spin-orbit coupling interaction can lead to the phase transition of the topological insulator, and the spin-orbit coupling interaction is more and more important in the condensed state. The size of the spin-orbit coupling interaction is proportional to the number of atomic nuclei, so the larger the atomic number, the greater the interaction of the spin-orbit coupling. As a result, for the compounds of the sixth cycle and the elements of the fifth cycle, we need to consider the spin-orbit coupling interaction. The 5d transition metal oxide is extended in real-space distribution compared to the 3d and 4d systems, so the electron association U is relatively 3d, The 4d transition element is relatively small. It is contemplated that the system will be changed from the insulator to the metal from 3d to 5d. However, many 5d system exhibit insulator behavior since that 5-d transition group element tend to have strong spin-orbit coupling interaction. The 5-d transition metal oxide contains rich physics under the condition of the interaction of the spin-orbit coupling and the electron correlation and the interaction of the lattice. Such as mott insulators, complex magnetic, topological insulators, weyl semi-metals, and the like. For heavy elements Bi, Pb, Te, Sb, Sn, and the like, their spin-orbit coupling interaction is also strong, so many topological insulators contain these heavy elements, such as HgTe/ CdTe quantum wells, Bi2Se3, and the like. In addition to the topological insulator, a topology-protected semi-metal is also found. The topology semi-metal is now divided into three groups: Dirac semi-metal, Weyl half-metal, and node-line semi-metal. The Dirac point and the Weyl point in the Dirac semi-metal and the Weyl semi-metal are distributed discretely in the momentum space and the number is limited. Their surface states are characterized by a fermi arc. The Dirac semimetal is transformed into Weyl semimetal at break time inversion or space inversion symmetry. While the energy bands of the node-line semi-metal intersect in the vicinity of the fermi surface and the intersection point has a plurality of intersection points which are connected in a line in the reverse space. For the ideal node-line half-metal, all the intersections are on the same energy plane, then its surface state is a flat band. This provides a platform for the study of superconducting and fractional quantum Hall effects. It is of great significance to find the material of the strong spin-orbit-coupled interaction system and to study the rich physical properties of these materials. Based on the density functional theory, the tight-binding model and the k-p perturbation theory, we study the material of several kinds of strong spin-orbit coupling: we first study the 5-d transition metal compound, NaOO3, and find that it is a new three-dimensional Slater insulator. We have systematically calculated the electronic structure of NaOO3 and searched its magnetic structure and found that its magnetic ground state is G-type anti-ferromagnetic. The spin-orbit coupling interaction does not allow the system to open the energy gap, and the same electron correlation does not allow the system to open the energy gap. When the system is in the G-type antiferromagnetic state, an energy gap is opened, which proves that NaOO3 is a three-dimensional Slater insulator. The magnetic structure of our theory is then confirmed by the experiment. Secondly, we have predicted a new three-dimensional Dirac semimetal BaYBi (Y = Cu, Ag, Au). This kind of Dirac semi-metallic material is stable, the composition is not highly toxic, and it brings great convenience for experimental research and industrial application. The electron structure of BaCuBi and BaAgBi is similar to that of BaAgBi: the 6p band of Bi forms a reverse band structure through the Ag-5s (Cu-4s) band at the r point under the combination of the spin-orbit coupling interaction and the crystal field, and the intersection point (Dirac point) is formed along the F-A. While the anti-tape structure of the baaubi occurs between the 6p bands of bi. We have also discussed doping so that this three-dimensional Dirac semimetal becomes a Weyl semi-metal. Then we discussed the electronic structure and surface state of Weyl semi-metal NbP. NbP is a member of the recently discovered non-center-inverted Weyl semi-metallic TaAs family. When the NbP is coupled without a spin-free track, the energy band forms a node-line under mirror symmetry protection. When the spin-orbit coupling interaction is taken into account, each node-line evolves into an opposing Weyl point. Their surface state has a particular tadpole shape. Our theoretical calculation results are in good agreement with the results of the ARPES experiment. By selecting a closed curve and looking at the number of times this closed curve crosses the Fermi surface, we finally determine that NbP is a Weyl half-metal. In the end, we find that the binary compound CaTe of the CsCl structure is a node-line semi-metal when the spin-orbit coupling interaction is neglected. It has three mutually perpendicular node-lines, and the three nodes-line are all near the M-point. We studied the surface state of the node-line semi-metal, and found that its surface state is the same two-dimensional flat belt as the drum surface. This provides a platform for the study of superconducting and fractional quantum Hall effects. When the spin-orbit coupling interaction is applied, this topology node-line half-metal becomes a Dirac semi-metal. The three node-line of it will open the energy gap, leaving the intersection only on the M-R line. This intersection is stabilized by the symmetry of the C4 rotation symmetry on the M-R line. If the C4 rotational symmetry is broken, such as the addition of stress, then this three-dimensional Dirac semi-metal will evolve into a strong topological insulator.
【学位授予单位】：南京大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O469

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