具有自旋—軌道耦合的關(guān)聯(lián)體系中的拓?fù)湎嘁约靶缕媪孔蝇F(xiàn)象的研究
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本文關(guān)鍵詞：具有自旋—軌道耦合的關(guān)聯(lián)體系中的拓?fù)湎嘁约靶缕媪孔蝇F(xiàn)象的研究 出處：《南京大學(xué)》2016年博士論文 論文類型：學(xué)位論文
更多相關(guān)文章： 自旋-軌道Mott絕緣體 Kitaev模型 拓?fù)湎?/b> 量子自旋液體 量子相變
【摘要】：在最近的研究領(lǐng)域里,具有強(qiáng)自旋-軌道耦合的Mott絕緣體作為一個主要興趣點已經(jīng)顯現(xiàn)出來,例如可能具有新奇磁序以及拓?fù)渥孕后w的5d過渡金屬氧化物。在這些候選材料中,銥化物,例如Sr2IrO4, A2IrO3 (A=Na, Li),以及最近合成的α-RuCl3已經(jīng)明顯的吸引了很多關(guān)注,原因在于它們是(1)探測強(qiáng)自旋-軌道耦合與Mott物理相互影響的理想平臺,以及(2)可能實現(xiàn)著名的Kitaev物理的候選材料。定義在蜂窩格子上的自旋1/2 Kitaev模型可以嚴(yán)格求解而且基態(tài)是自旋液體。這個模型具有Z2拓?fù)湫?而且自旋磁矩會分?jǐn)?shù)化為Majorana費米子以及Z2規(guī)范場激發(fā)。Kitaev自旋液體與傳統(tǒng)的RVB自旋液體的最重要區(qū)別之一在于自旋旋轉(zhuǎn)對稱性,也就是說,后者具有最大的SU(2)自旋對稱性,但是前者只有最小的Q8自旋對稱性。而就在最近,人們認(rèn)識到所謂的Kitaev-Heisenberg模型是可能抓住自旋-軌道Mott絕緣體基本物理的最重要模型之一。(1)我們利用對稱性分析,給出了帶有自旋-軌道耦合項的Kane-Mele模型哈密頓量的詳細(xì)推導(dǎo)。推導(dǎo)過程用到了四種對稱性：時間反演對稱性,晶格的鏡像對稱性,晶格的二度以及三度旋轉(zhuǎn)對稱性。我們的計算表明,這些對稱性會使得很多二次量子化矩陣元嚴(yán)格等于0,從而最終得到簡單的Kane-Mele模型表達(dá)式。同樣的對稱性分析也可以給出Kagome格子上自旋-軌道耦合的二次量子化表達(dá)式。值得注意的是,Kagome格子的自旋-軌道耦合中存在最近鄰的跳躍項,原因是：對于Kagome格子,對稱性禁止相同子格之間的所有跳躍。這個和蜂窩格子上的Kane-Mele模型正好相反,其對稱性禁止不同子格之間的自旋-軌道耦合跳躍。(2)我們研究了三角格子上的Kitaev-Heisenberg模型在未摻雜以及摻雜情況下的可能基態(tài)。對于未摻雜系統(tǒng),結(jié)合嚴(yán)格對角化數(shù)值計算以及四子格變換分析可以給出一個可能的奇特相以及四個磁有序相,其中包括共線排列的條紋磁序相以及非共線排列的螺旋磁序相。利用Schwinger費米子平均場方法進(jìn)一步研究反鐵磁Kitaev點附近的那個奇特相,我們得到了一個能量穩(wěn)定,陳數(shù)為士2的Z2手性自旋液體。對于有限摻雜的情況,我們發(fā)現(xiàn)反鐵磁Heisenberg相互作用有利于s波超導(dǎo)和d+id波超導(dǎo),而反鐵磁Kitaev相互作用有利于d+id波超導(dǎo),鐵磁Kitaev相互作用有利于時間反演不變的拓?fù)鋚波超導(dǎo)。該工作首次給出了三角格子上量子Kitaev-Heisenberg模型的基態(tài)相圖。(3)我們研究了半滿時的具有Kitaev類型跳躍的三角格子Hubbard模型。利用變分cluster方法(VCA),我們在相圖中確定了5個相：金屬相,非共面手性磁序,120°磁序,非磁絕緣體(NMI),以及相互作用的陳絕緣體(CI)。無相互作用時,增強(qiáng)Kitaev類型跳躍會使系統(tǒng)從金屬相變到CI。隨著相互作用的增強(qiáng),CI到NMI的相變伴隨著電荷能隙從間接能隙變成直接能隙。相互作用的陳絕緣體具有一個非零陳數(shù)2。我們利用slave-rotor理論,指出NMI相可能包含一個無(自旋)能隙的Mott絕緣體和一個具有spinon邊緣態(tài)的分?jǐn)?shù)化的CI。我們的工作表明：能帶拓?fù)浜碗娮雨P(guān)聯(lián)的相互影響會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.
【學(xué)位授予單位】：南京大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O469
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