具有自旋—轨道耦合的关联体系中的拓扑相以及新奇量子现象的研究

发布时间：2018-01-01 14:27

本文关键词：具有自旋—轨道耦合的关联体系中的拓扑相以及新奇量子现象的研究　出处：《南京大学》2016年博士论文　论文类型：学位论文

【摘要】：在最近的研究领域里,具有强自旋-轨道耦合的Mott绝缘体作为一个主要兴趣点已经显现出来,例如可能具有新奇磁序以及拓扑自旋液体的5d过渡金属氧化物。在这些候选材料中,铱化物,例如Sr2IrO4, A2IrO3 (A=Na, Li),以及最近合成的α-RuCl3已经明显的吸引了很多关注,原因在于它们是(1)探测强自旋-轨道耦合与Mott物理相互影响的理想平台,以及(2)可能实现著名的Kitaev物理的候选材料。定义在蜂窝格子上的自旋1/2 Kitaev模型可以严格求解而且基态是自旋液体。这个模型具有Z2拓扑序,而且自旋磁矩会分数化为Majorana费米子以及Z2规范场激发。Kitaev自旋液体与传统的RVB自旋液体的最重要区别之一在于自旋旋转对称性,也就是说,后者具有最大的SU(2)自旋对称性,但是前者只有最小的Q8自旋对称性。而就在最近,人们认识到所谓的Kitaev-Heisenberg模型是可能抓住自旋-轨道Mott绝缘体基本物理的最重要模型之一。(1)我们利用对称性分析,给出了带有自旋-轨道耦合项的Kane-Mele模型哈密顿量的详细推导。推导过程用到了四种对称性：时间反演对称性,晶格的镜像对称性,晶格的二度以及三度旋转对称性。我们的计算表明,这些对称性会使得很多二次量子化矩阵元严格等于0,从而最终得到简单的Kane-Mele模型表达式。同样的对称性分析也可以给出Kagome格子上自旋-轨道耦合的二次量子化表达式。值得注意的是,Kagome格子的自旋-轨道耦合中存在最近邻的跳跃项,原因是：对于Kagome格子,对称性禁止相同子格之间的所有跳跃。这个和蜂窝格子上的Kane-Mele模型正好相反,其对称性禁止不同子格之间的自旋-轨道耦合跳跃。(2)我们研究了三角格子上的Kitaev-Heisenberg模型在未掺杂以及掺杂情况下的可能基态。对于未掺杂系统,结合严格对角化数值计算以及四子格变换分析可以给出一个可能的奇特相以及四个磁有序相,其中包括共线排列的条纹磁序相以及非共线排列的螺旋磁序相。利用Schwinger费米子平均场方法进一步研究反铁磁Kitaev点附近的那个奇特相,我们得到了一个能量稳定,陈数为士2的Z2手性自旋液体。对于有限掺杂的情况,我们发现反铁磁Heisenberg相互作用有利于s波超导和d+id波超导,而反铁磁Kitaev相互作用有利于d+id波超导,铁磁Kitaev相互作用有利于时间反演不变的拓扑p波超导。该工作首次给出了三角格子上量子Kitaev-Heisenberg模型的基态相图。(3)我们研究了半满时的具有Kitaev类型跳跃的三角格子Hubbard模型。利用变分cluster方法(VCA),我们在相图中确定了5个相：金属相,非共面手性磁序,120°磁序,非磁绝缘体(NMI),以及相互作用的陈绝缘体(CI)。无相互作用时,增强Kitaev类型跳跃会使系统从金属相变到CI。随着相互作用的增强,CI到NMI的相变伴随着电荷能隙从间接能隙变成直接能隙。相互作用的陈绝缘体具有一个非零陈数2。我们利用slave-rotor理论,指出NMI相可能包含一个无(自旋)能隙的Mott绝缘体和一个具有spinon边缘态的分数化的CI。我们的工作表明：能带拓扑和电子关联的相互影响会衍生出十分新奇的量子相。
[Abstract]:In recent research fields, with strong spin orbit coupling of the Mott insulator as a major point of interest has emerged, for example, may have a novel magnetic order and spin liquid topological transition metal oxide 5D. In these candidate materials, iridium compounds, such as Sr2IrO4, A2IrO3 (A=Na, Li), and recently alpha -RuCl3 synthesis has obviously attracted a lot of attention, the reason is that they are (1) an ideal platform for detecting the strong spin orbit coupling and Mott physical interaction, and (2) possible candidate materials for Kitaev physics. The famous 1/2 spin Kitaev model in a honeycomb lattice on the definition can be solved strictly and the ground state is this spin liquid. Z2 model with topological order, and will spin fractions to the Majorana fermion and gauge field Z2 the most important difference between the RVB and.Kitaev spin spin liquid excitation of traditional liquid One is the spin symmetry, that is to say, the latter has the largest SU (2) spin symmetry, but the former only minimal Q8 symmetry. But recently, people realize that the so-called Kitaev-Heisenberg model is one of the most important basic physical model can catch the spin orbit Mott insulator (1). We use the symmetry analysis, gives a detailed derivation of the Kane-Mele model Hamiltonian with spin orbit coupling term. The derivation process used in the four kinds of symmetries: time reversal symmetry, mirror symmetry lattice, the lattice of two degrees and three degrees rotation symmetry. Our calculations show that these symmetries will make a lot of the two quantization matrix element is exactly equal to 0, and finally get the Kane-Mele model simple expressions. The symmetry analysis also can be given two times on the Kagome lattice quantization of spin orbit coupling Expression. It is worth noting that the Kagome lattice spin orbit coupling in the presence of nearest neighbor jumps, the reason is: for the Kagome lattice symmetry prohibits all jumps between same sub lattices. The Kane-Mele model and the honeycomb lattice on the contrary, the symmetry no jumping spin orbit between different sub lattices coupling. (2) we studied the possible ground state Kitaev-Heisenberg model on the triangular lattice in undoped and doped condition. For the undoped system analysis can give a possible strange phase and four magnetic ordering combined with exact diagonalization of numerical calculation and four sub lattice transformation, including magnetic stripe order collinear arrangement the spiral magnetic ordering phase and non collinear phase arrangement. Further study near the antiferromagnetic Kitaev point of the odd phase using Schwinger fermion mean field method, we can get a The amount of stable Z2 chiral spin liquid Chen Shu + 2. The co doping case, we found that the antiferromagnetic interaction between Heisenberg to S wave superconductor and d+id wave superconductivity, and antiferromagnetic interaction between Kitaev to d+id wave superconductor, Kitaev ferromagnetic interaction topology P wave superconductor for time reversal invariant the work is given for the first time. The ground state phase diagram of the quantum Kitaev-Heisenberg model on the triangular lattice. (3) we studied with a triangular lattice Hubbard model for Kitaev type jump is half full. By using the variational cluster method (VCA), we identified 5 phases in the phase diagram: metal phase, chiral non coplanar magnetic ordering 120 degrees, magnetic order, non magnetic insulator (NMI), and the interaction of Chen insulator (CI). No interaction, enhanced Kitaev type jump will enable the system from the metal phase transition to enhance interaction with CI., CI to NMI transformation with electricity Energetic gap from indirect bandgap into direct bandgap. The interaction of Chen insulator has a nonzero Chen Shu 2. we use slave-rotor theory, pointed out that the NMI phase may contain a (spin) Mott insulator energy gap and a spinon edge state of scores of the CI. of our work show that each other effect of band topology and electron correlation will be derived from quantum very strange.

【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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