拓扑绝缘体材料铁磁性及表面态的调控
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摘要
拓扑绝缘体作为一种新发现的量子物态,具有奇异的物理性质,并在自旋电子学和量子计算等方面有着潜在的重大应用价值。拓扑绝缘体的体电子结构为有带隙的绝缘体,但表面或边界却为无带隙的金属态。拓扑绝缘体材料中表面带隙的打开是实现许多奇异现象的必要条件,而杂质元素掺杂引入铁磁序是破坏拓扑绝缘体时间反演对称性从而打开表面带隙的重要方法。例如,通过在Bi2Se3、 Bi2Te3或Sb2Te3中引入过渡金属元素(Fe或者Cr)可以实现一类最基本的破坏了时间反演对称性的二维磁性拓扑绝缘体,并且只要具备适当的温度和掺杂浓度等条件,薄膜体系就可以实现量子反常霍尔效应。最近,该理论预言已得到实验的证实。
目前,已有大量的拓扑绝缘体材料被人们预言和证实。在这众多拓扑绝缘体材料中,具有较大体带隙和最简单表面Dirac能谱的Bi2Te3, Bi2Se3和Sb2Te3引起了人们广泛的关注。然而可制备的Bi2Te3, Bi2Se3和Sb2Te3中却存在着大量的本征缺陷,并且Bi2Te3的Dirac点位于表面的费米能级以下,这就大大阻碍了该类拓扑绝缘体材料中奇异物理现象的实现以及它们在器件制备中的应用。因此,如何抑制Bi2Te3, Bi2Se3和Sb2Te3的本征缺陷并实现对电子结构等的有效调控成为了该研究领域亟待解决的问题。此外,T1BiTe2(T1BiSe2)和Bi2Te2Se由于分别具有较为理想的Dirac锥和较大的体电阻也引起了人们较为广泛的关注。
本文中,我们系统地研究了拓扑绝缘体材料铁磁性和表面态的调控,并针对实验上具有争议的一些问题给出了合理的解释。本论文共分为七章。第一章简要介绍了拓扑绝缘体的特征及发展历程。第二章介绍了密度泛函理论并对文中所采用的第一性原理计算软件包做了说明。第三章介绍了几何相位和d0磁性。第四章分节阐述了过渡金属元素以及2p轻元素单掺、共掺等对拓扑绝缘体材料铁磁性和表面态的调控,并讨论了量子反常霍尔效应等奇异现象在拓扑绝缘体薄膜中实现的可能性。第五章研究了T1Bi(S1-xSex)2和(Bi1-xSbx)2Te3固溶体体系中的拓扑相变和表面态调控。第六章探索研究了应力和自旋轨道耦合在拓扑晶绝缘体材料实现中的作用。第七章对本文的研究内容做了总结,并指出了拓扑绝缘体研究领域亟待解决的问题以及后续的研究计划。本文的研究内容和主要结论如下所述：
(1)研究了旋转磁场中相互作用自旋1/2两粒子体系的几何相位,证明了非局域相互作用不影响态的可分离性的可能性,并给出了使该自旋1/2两粒子体系的初始分离态保持可分离性的充分必要条件,此时该相互作用自旋1/2两粒子体系的总几何相在任意时刻均等于其子体系几何相的和。
(2)基于密度泛函理论,研究了C在Mg3N2两不等价N位置替位时的电子结构和自旋极化性质。研究结果表明C在两个不等价N位置均能引入1.0μB磁矩,但其电子结构却因两不等价N位置的局域几何结构和对称性不同而相差较大。进一步研究表明C掺杂Mg3N2中能够实现较为稳定的铁磁耦合。
(3)研究了过渡金属元素Mn掺杂Bi2Te3的磁耦合特性及其对拓扑表面态的调控作用。研究结果表明Mn在Bi位置的替位掺杂能够在体系中引入自旋极化的隙态以及4.0μB磁矩,并且体系中足够的空穴载流子浓度是引入局域自旋磁矩的必要条件。掺杂元素Mn间的超交换作用是Mn掺杂Bi2Te3体系中形成稳定铁磁性的来源。引入的铁磁序会破换体系的时间反演对称性,并在原Dirac点位置打开带隙。
(4)首次开展了2p轻元素X(X=B,C和N)对拓扑绝缘体材料V2VI3(V=Bi和Sb,VI=Se和Te)的磁耦合特性及拓扑表面态的调控作用的研究。研究结果表明X在阴离子位置的替位掺杂能够在体系中形成稳定的铁磁序并在表面Dirac点处打开带隙。掺杂的轻元素X具有足够局域化的2p轨道是X掺杂V2VI3中形成稳定的磁性基态的必要条件。足够局域化的2p轨道与体系中X-V键长息息相关,而X-V键长则主要由掺杂位置的周围环境、离子半径以及掺杂元素X与V2VI3阴离子的相对电负性强度所决定。
(5)探讨了三元拓扑绝缘体材料Bi2Te2Se中实现可调表面和绝缘有质量Dirac费米子态的可能性。研究表明,O替位Bi2Te2Se (111)表面最外层的Te能够对表面进行有效调节,并实现理想的Dirac锥。Cr和O在Bi2Te2Se中Bi和Te位置共掺则不仅能使体系原Dirac点上升至体带隙,还可以在原Dirac点打开带隙,并使费米能级位于体带隙和表面带隙中,从而实现绝缘有质量Dirac费米子态。此外,Bi2Te2Se中Mn和F在Bi和Te位置共掺也可以在非理想Dirac锥的情况下实现绝缘有质量Dirac费米子态。
(6)从理论上证明了拓扑绝缘体材料Bi2Te3中磁性和非磁性元素共掺是实现绝缘有质量Dirac费米子态的有效方法。M(M=Ti,V,Cr,Mn和Fe)替位Bi可在Bi2Te3(111)表面中引入垂直于平面的磁矩,在Dirac点打开带隙,但此时表面中仍有许多能带穿过费米能级。0替位(111)表面最外层的Te能够对表面进行有效调节,并使其Dirac点上移至体带隙中,从而实现理想的Dirac锥。Fe/O在Bi2Te3中的共同作用则不仅可以在Dirac点打开带隙,还可以使费米能级位于体带隙和表面带隙中,从而在Bi2Te3中实现绝缘有质量Dirac费米子态。
(7)研究了三元拓扑绝缘体材料T1BiTe2和T1BiSe2中实现量子反常霍尔效应的可能性。研究结果表明具有铁磁性的拓扑绝缘体薄膜的霍尔电导在一定条件下可被量子化。在杂质元素Ti,Cr,Fe和Au中,Cr在T1和Bi位置替位掺杂均不会引入载流子,并可以实现稳定的铁磁基态,是T1BiTe2和T1BiSe2中实现量子反常霍尔效应的最理想的掺杂材料。
(8)基于第一性原理计算和有效哈密顿量模型分析,从理论上研究了T1Bi(S--xSex)2固溶体从传统绝缘体到拓扑绝缘体的拓扑相变以及没有破坏时间反演对称性时表面带隙的引入。研究表明T1Bi(S1-xSex)2固溶体中自旋轨道耦合强度和晶格参数的改变是固溶体体系发生拓扑相变的根本原因,而自旋轨道耦合强度和晶格参数的改变则是由Se浓度x的变化所引起的。Dirac锥在体系是否破坏空间反演对称性时完全不同,并且空间反演对称的破坏会在原Dirac点位置打开带隙。我们的研究为最近实验[Science332,560(2011); Nat. Phys.7,840(2011)]中观察到的不同现象提供了理论解释及证明。
(9)研究了固溶体(Bi1-xSbx)2Te3中绝缘的体电子态及可调节Dirac锥的实现,这对拓扑绝缘体在自旋电子学和量子计算等方面的应用具有非常重要的意义。研究结果表明,任意浓度x的(Bi1-xSbx)2Te3中均会发生能带反转,即实现了一系列非平庸的拓扑绝缘体。并且伴随着Sb浓度x的增加,狄拉克点一直向上移动直到位于体能隙内。此外,随着x的增大,(Bi1-xSbx)2Te3中的本征缺陷越来越难以形成,从而实现了具有真正绝缘体电子态的拓扑绝缘体材料。
(10)以SnTe和PbTe为例系统地研究了应力及自旋轨道耦合在实现拓扑晶绝缘体材料中的作用。研究结果表明,在不考虑自旋轨道耦合作用而仅仅在应力的作用下,SnTe和PbTe中也能实现能带反转。然而,自旋轨道耦合对拓扑晶绝缘体的形成却必不可少,并且它还可以促进体系能带反转的实现。拓扑表面态的研究表明表面态性质与薄膜厚度息息相关,并且Dirac点随着厚度变化既可以位于镜像对称点也可以稍微远离镜像对称点。我们的研究结果对新的拓扑晶绝缘体的实现具有重要意义。
以上研究结果阐明了杂质对拓扑绝缘体材料电子结构、自旋结构及相关性质的调控机理及作用规律,给出了引入拓扑绝缘体表面带隙以及实现量子反常霍尔效应等奇异现象的有效方法,揭示了拓扑晶绝缘体实现的条件及影响因素。我们的研究不仅能丰富人们对拓扑绝缘体材料相关性质的认识和理解,为自旋电子学等的发展提供重要的信息,而且对构建新量子态方面也具有重要的意义。
The discovered topological insulator (TI) exhibits a bulk energy gap and gapless metallic surface state, composing a novel quantum state of matter in condensed matter physics. Owing to its exotic physical properties and potential technological applications in spintromcs and quantum computing, TI has been at the core of a very active research area. The time-reversal symmetry breaking perturbation, such as the magnetic doping, can open up an energy gap at the original Dirac point of the topological surface state, and this gap is essential to a range of striking phenomena. For instance, Fe-and Cr-doped Bi2Se3, Bi2Te3, and Sb2Te3realize the two-dimensional magnetic TIs that break the time-reversal symmetry, and the quantum anomalous Hall effect is very likely to occur in the two-dimensional magnetic TIs, which has been recently observed in experiments.
Since then, many TIs have been theoretically proposed and experimentally demonstrated, and the three-dimensional TIs Bi2Se3, Bi2Te3, and Sb2Te3have become the model materials due to their exceptional properties of possessing relatively large bulk band gaps and one single Dirac cone at the Dirac point in Brillouin zone. However, the currently available Bi2Se3, Bi2Te3, and Sb2Te3always show unacceptably high bulk conductivity introduced by the strong native defects, and the Dirac point of Bi2Te3(111) surface lies below the Fermi level and is buried in the bulk valence band. This challenges the realization of the striking phenomena and possibility of being functional components of electronic devices. Therefore, immense efforts are needed to solve the problems. In addition, T1BiTe2(T1BiSe2) and Bi2Te2Se have attracted much interest due to the more ideal Dirac cone and larger bulk resistivity than previously studied TIs, respectively.
In this dissertation, we systematically investigate the manipulation of ferromagnetism and surface states in TIs, and give some reasonable explanations for some controversial issues in experiments. The dissertation is divided into seven chapters. In the first chapter, we introduce the TIs family. In the second chapter, we introduce the density functional theory and give a brief description for the first-principles software packages. In the third chapter, the geometric phase and the d0ferromagnetism are studied. In the fourth chapter, we investigate the manipulation of ferromagnetism and surface states in doped TIs, as well as the realization of the quantum anomalous Hall effect. In the fifth chapter, the topological phase transition and modulated topological surface states in solid solution T1Bi(S1-xSex)2and (Bi1-xSbx)2Te3are explored. In the sixth chapter, we further investigate the role of strain and spin-orbit coupling (SOC) in realization of topological crystalline insulators. In the seventh chapter, a summarization of the contents, several open problems in TIs, and the further research plan are given. The main contents and conclusions are listed as follows:
(1) The geometric phase of two interacting spin-half particles in a rotating magnetic field is studied. It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. We illustrate this point by investigating a well-known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.
(2) Based on density functional theory, we investigate the electronic and spin-polarized properties of C-doped Mg3N2with C at two nonequivalent N sites. Results of our calculations reveal that the electronic properties are sensitive to the local structures and symmetries of doping sites while the magnetic moment is not. The substitution of C by N favors a spin-polarized state with a total magnetic moment of1.0μB per C, which is equal to the number of holes in the system. Our magnetic coupling calculations also indicate that substantial ferromagnetism is possible in the C-doped Mg3N2.
(3) The ferromagnetism and topological surface states manipulated by Mn in TI Bi2Te3are investigated. Our results indicate that substitution Mn for Bi can induce spin-polarized hole states with a total magnetic moments of4.0μB, and sufficient hole carrier density is required to obtain sustained magnetization. The obvious gap at the Dirac point coinciding with sharp surface state appears as Mn doped into Bi2Te3because the magnetic interactions break the time reversal symmetry.
(4) The manipulation effects by doping of2p light elements X (X=B, C, and N) on topological surface states in V2VI3(V=Bi and Sb, VI=Se and Te) are systemically explored. Our results unveil that X doping at anion sites can induce magnetic moments and gap opening at the Dirac point. To have a stable magnetic ground state, the dopant2p states must be sufficiently localized, which closely depends on the X-V bond lengths. In addition, the X-V bond length in X-doped V2VI3mainly depends on three factors:(1) the bonding environment of doping sites,(2) sizes of atoms, and (3) differences in their electronegativities.
(5) We explore the possibility of modifying the topological surface states and achieving the insulating massive Dirac fermion state in ternary TI Bi2Te2Se. Substitution of O for the outmost-layer Te leads to tunable surface states with an ideal Dirac cone. The co-substitution of Cr and O, as well as that of Mn and F, for the surface Bi and Te places the Dirac point inside the bulk band gap and opens a band gap at the Dirac point, hence creating the insulating massive Dirac fermion state.
(6) We theoretically reveal that co-substitution of magnetic and non-magnetic elements is a promising way to realize the insulating massive Dirac fermion state, and Fe is the best candidate to achieve it in Bi2Te3among M (M=Ti, V, Cr, Mn, and Fe). Substitution of M for Bi introduces perpendicular magnetism, but some energy bands cross the Fermi level. Furthermore, the synergistic effect of Fe and O places the Dirac point inside the bulk band gap and opens a surface band gap at the Dirac point with the Fermi level inside it.
(7) The occurrence of quantum anomalous Hall effect in ternary TIs TIBiTe2and T1BiSe2is predicted. The effective Hamiltonian analysis shows that the Hall conductance of the2D ferromagnetic TIs TF can be quantized. The first-principle calculations reveal that Cr is the best candidate to induce the ferromagnetic order in the insulating phase among X (X=Ti, Cr, Fe, and Au). The magnetic order in insulating phase arises from the spin polarization of substitutional Cr atoms and the free carriers are not needed for the formation of the substantial ferromagnetic coupling.
(8) Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TIBi(S1-xSex)2.The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band gap can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Science332,560(2011); Nat. Phys.7,840(2011)].
(9) We present theoretical evidence for modulating the topological surface states and achieving the insulating bulk states in solid-solution (Bi1-xSbx)2Te3. This is very important for applications of TIs in spintronics and quantum computation. Our results reveal that the band inversion occurs in (Bi1-xSbx)2Te3, indicating the non-triviality across the entire composition range, and the Dirac point moves upwards till it lies within the bulk energy gap accompanying the increase of Sb concentration x. In addition, with increasing x, the formation of prominent native defects becomes much more difficult, resulting in the truly insulating bulk.
(10) Here, using SnTe and PbTe as the examples, we give detailed insight into theeffects of SOC and strain on the formation of the topological crystalline insulator. A strain-induced band inversion, without any SOC, is shown. The SOC, however, is indispensable for achieving the topological crystalline insulator phase in real materials and can promote the process of the band inversion. Detailed surface state analysis reveals that topological surface state is thickness dependent and the Dirac point can locate precisely on or slightly away from the mirror-symmetry point. Our results pave a way of the material realization of new topological crystalline insulator.
The research results reveal the mechanism and effect rules of electronic structures, spin polarization, and related properties of doped TIs, provide the way of the surface gap opening and quantum anomalous Hall effect realization, and show the criteria of the material realization of new topological crystalline insulator. The studies pave the way to explore the fundamental physics phenomena and spintronic device applications of TIs, and are also helpful to discover the novel quantum states.
目前,已有大量的拓扑绝缘体材料被人们预言和证实。在这众多拓扑绝缘体材料中,具有较大体带隙和最简单表面Dirac能谱的Bi2Te3, Bi2Se3和Sb2Te3引起了人们广泛的关注。然而可制备的Bi2Te3, Bi2Se3和Sb2Te3中却存在着大量的本征缺陷,并且Bi2Te3的Dirac点位于表面的费米能级以下,这就大大阻碍了该类拓扑绝缘体材料中奇异物理现象的实现以及它们在器件制备中的应用。因此,如何抑制Bi2Te3, Bi2Se3和Sb2Te3的本征缺陷并实现对电子结构等的有效调控成为了该研究领域亟待解决的问题。此外,T1BiTe2(T1BiSe2)和Bi2Te2Se由于分别具有较为理想的Dirac锥和较大的体电阻也引起了人们较为广泛的关注。
本文中,我们系统地研究了拓扑绝缘体材料铁磁性和表面态的调控,并针对实验上具有争议的一些问题给出了合理的解释。本论文共分为七章。第一章简要介绍了拓扑绝缘体的特征及发展历程。第二章介绍了密度泛函理论并对文中所采用的第一性原理计算软件包做了说明。第三章介绍了几何相位和d0磁性。第四章分节阐述了过渡金属元素以及2p轻元素单掺、共掺等对拓扑绝缘体材料铁磁性和表面态的调控,并讨论了量子反常霍尔效应等奇异现象在拓扑绝缘体薄膜中实现的可能性。第五章研究了T1Bi(S1-xSex)2和(Bi1-xSbx)2Te3固溶体体系中的拓扑相变和表面态调控。第六章探索研究了应力和自旋轨道耦合在拓扑晶绝缘体材料实现中的作用。第七章对本文的研究内容做了总结,并指出了拓扑绝缘体研究领域亟待解决的问题以及后续的研究计划。本文的研究内容和主要结论如下所述：
(1)研究了旋转磁场中相互作用自旋1/2两粒子体系的几何相位,证明了非局域相互作用不影响态的可分离性的可能性,并给出了使该自旋1/2两粒子体系的初始分离态保持可分离性的充分必要条件,此时该相互作用自旋1/2两粒子体系的总几何相在任意时刻均等于其子体系几何相的和。
(2)基于密度泛函理论,研究了C在Mg3N2两不等价N位置替位时的电子结构和自旋极化性质。研究结果表明C在两个不等价N位置均能引入1.0μB磁矩,但其电子结构却因两不等价N位置的局域几何结构和对称性不同而相差较大。进一步研究表明C掺杂Mg3N2中能够实现较为稳定的铁磁耦合。
(3)研究了过渡金属元素Mn掺杂Bi2Te3的磁耦合特性及其对拓扑表面态的调控作用。研究结果表明Mn在Bi位置的替位掺杂能够在体系中引入自旋极化的隙态以及4.0μB磁矩,并且体系中足够的空穴载流子浓度是引入局域自旋磁矩的必要条件。掺杂元素Mn间的超交换作用是Mn掺杂Bi2Te3体系中形成稳定铁磁性的来源。引入的铁磁序会破换体系的时间反演对称性,并在原Dirac点位置打开带隙。
(4)首次开展了2p轻元素X(X=B,C和N)对拓扑绝缘体材料V2VI3(V=Bi和Sb,VI=Se和Te)的磁耦合特性及拓扑表面态的调控作用的研究。研究结果表明X在阴离子位置的替位掺杂能够在体系中形成稳定的铁磁序并在表面Dirac点处打开带隙。掺杂的轻元素X具有足够局域化的2p轨道是X掺杂V2VI3中形成稳定的磁性基态的必要条件。足够局域化的2p轨道与体系中X-V键长息息相关,而X-V键长则主要由掺杂位置的周围环境、离子半径以及掺杂元素X与V2VI3阴离子的相对电负性强度所决定。
(5)探讨了三元拓扑绝缘体材料Bi2Te2Se中实现可调表面和绝缘有质量Dirac费米子态的可能性。研究表明,O替位Bi2Te2Se (111)表面最外层的Te能够对表面进行有效调节,并实现理想的Dirac锥。Cr和O在Bi2Te2Se中Bi和Te位置共掺则不仅能使体系原Dirac点上升至体带隙,还可以在原Dirac点打开带隙,并使费米能级位于体带隙和表面带隙中,从而实现绝缘有质量Dirac费米子态。此外,Bi2Te2Se中Mn和F在Bi和Te位置共掺也可以在非理想Dirac锥的情况下实现绝缘有质量Dirac费米子态。
(6)从理论上证明了拓扑绝缘体材料Bi2Te3中磁性和非磁性元素共掺是实现绝缘有质量Dirac费米子态的有效方法。M(M=Ti,V,Cr,Mn和Fe)替位Bi可在Bi2Te3(111)表面中引入垂直于平面的磁矩,在Dirac点打开带隙,但此时表面中仍有许多能带穿过费米能级。0替位(111)表面最外层的Te能够对表面进行有效调节,并使其Dirac点上移至体带隙中,从而实现理想的Dirac锥。Fe/O在Bi2Te3中的共同作用则不仅可以在Dirac点打开带隙,还可以使费米能级位于体带隙和表面带隙中,从而在Bi2Te3中实现绝缘有质量Dirac费米子态。
(7)研究了三元拓扑绝缘体材料T1BiTe2和T1BiSe2中实现量子反常霍尔效应的可能性。研究结果表明具有铁磁性的拓扑绝缘体薄膜的霍尔电导在一定条件下可被量子化。在杂质元素Ti,Cr,Fe和Au中,Cr在T1和Bi位置替位掺杂均不会引入载流子,并可以实现稳定的铁磁基态,是T1BiTe2和T1BiSe2中实现量子反常霍尔效应的最理想的掺杂材料。
(8)基于第一性原理计算和有效哈密顿量模型分析,从理论上研究了T1Bi(S--xSex)2固溶体从传统绝缘体到拓扑绝缘体的拓扑相变以及没有破坏时间反演对称性时表面带隙的引入。研究表明T1Bi(S1-xSex)2固溶体中自旋轨道耦合强度和晶格参数的改变是固溶体体系发生拓扑相变的根本原因,而自旋轨道耦合强度和晶格参数的改变则是由Se浓度x的变化所引起的。Dirac锥在体系是否破坏空间反演对称性时完全不同,并且空间反演对称的破坏会在原Dirac点位置打开带隙。我们的研究为最近实验[Science332,560(2011); Nat. Phys.7,840(2011)]中观察到的不同现象提供了理论解释及证明。
(9)研究了固溶体(Bi1-xSbx)2Te3中绝缘的体电子态及可调节Dirac锥的实现,这对拓扑绝缘体在自旋电子学和量子计算等方面的应用具有非常重要的意义。研究结果表明,任意浓度x的(Bi1-xSbx)2Te3中均会发生能带反转,即实现了一系列非平庸的拓扑绝缘体。并且伴随着Sb浓度x的增加,狄拉克点一直向上移动直到位于体能隙内。此外,随着x的增大,(Bi1-xSbx)2Te3中的本征缺陷越来越难以形成,从而实现了具有真正绝缘体电子态的拓扑绝缘体材料。
(10)以SnTe和PbTe为例系统地研究了应力及自旋轨道耦合在实现拓扑晶绝缘体材料中的作用。研究结果表明,在不考虑自旋轨道耦合作用而仅仅在应力的作用下,SnTe和PbTe中也能实现能带反转。然而,自旋轨道耦合对拓扑晶绝缘体的形成却必不可少,并且它还可以促进体系能带反转的实现。拓扑表面态的研究表明表面态性质与薄膜厚度息息相关,并且Dirac点随着厚度变化既可以位于镜像对称点也可以稍微远离镜像对称点。我们的研究结果对新的拓扑晶绝缘体的实现具有重要意义。
以上研究结果阐明了杂质对拓扑绝缘体材料电子结构、自旋结构及相关性质的调控机理及作用规律,给出了引入拓扑绝缘体表面带隙以及实现量子反常霍尔效应等奇异现象的有效方法,揭示了拓扑晶绝缘体实现的条件及影响因素。我们的研究不仅能丰富人们对拓扑绝缘体材料相关性质的认识和理解,为自旋电子学等的发展提供重要的信息,而且对构建新量子态方面也具有重要的意义。
The discovered topological insulator (TI) exhibits a bulk energy gap and gapless metallic surface state, composing a novel quantum state of matter in condensed matter physics. Owing to its exotic physical properties and potential technological applications in spintromcs and quantum computing, TI has been at the core of a very active research area. The time-reversal symmetry breaking perturbation, such as the magnetic doping, can open up an energy gap at the original Dirac point of the topological surface state, and this gap is essential to a range of striking phenomena. For instance, Fe-and Cr-doped Bi2Se3, Bi2Te3, and Sb2Te3realize the two-dimensional magnetic TIs that break the time-reversal symmetry, and the quantum anomalous Hall effect is very likely to occur in the two-dimensional magnetic TIs, which has been recently observed in experiments.
Since then, many TIs have been theoretically proposed and experimentally demonstrated, and the three-dimensional TIs Bi2Se3, Bi2Te3, and Sb2Te3have become the model materials due to their exceptional properties of possessing relatively large bulk band gaps and one single Dirac cone at the Dirac point in Brillouin zone. However, the currently available Bi2Se3, Bi2Te3, and Sb2Te3always show unacceptably high bulk conductivity introduced by the strong native defects, and the Dirac point of Bi2Te3(111) surface lies below the Fermi level and is buried in the bulk valence band. This challenges the realization of the striking phenomena and possibility of being functional components of electronic devices. Therefore, immense efforts are needed to solve the problems. In addition, T1BiTe2(T1BiSe2) and Bi2Te2Se have attracted much interest due to the more ideal Dirac cone and larger bulk resistivity than previously studied TIs, respectively.
In this dissertation, we systematically investigate the manipulation of ferromagnetism and surface states in TIs, and give some reasonable explanations for some controversial issues in experiments. The dissertation is divided into seven chapters. In the first chapter, we introduce the TIs family. In the second chapter, we introduce the density functional theory and give a brief description for the first-principles software packages. In the third chapter, the geometric phase and the d0ferromagnetism are studied. In the fourth chapter, we investigate the manipulation of ferromagnetism and surface states in doped TIs, as well as the realization of the quantum anomalous Hall effect. In the fifth chapter, the topological phase transition and modulated topological surface states in solid solution T1Bi(S1-xSex)2and (Bi1-xSbx)2Te3are explored. In the sixth chapter, we further investigate the role of strain and spin-orbit coupling (SOC) in realization of topological crystalline insulators. In the seventh chapter, a summarization of the contents, several open problems in TIs, and the further research plan are given. The main contents and conclusions are listed as follows:
(1) The geometric phase of two interacting spin-half particles in a rotating magnetic field is studied. It is known that an interacting bipartite system evolves as an entangled state in general, even if it is initially in a separable state. Due to the entanglement of the state, the geometric phase of the system is not equal to the sum of the geometric phases of its two subsystems. However, there may exist a set of states in which the nonlocal interaction does not affect the separability of the states, and the geometric phase of the bipartite system is then always equal to the sum of the geometric phases of its subsystems. We illustrate this point by investigating a well-known physical model. We give a necessary and sufficient condition in which a separable state remains separable so that the geometric phase of the system is always equal to the sum of the geometric phases of its subsystems.
(2) Based on density functional theory, we investigate the electronic and spin-polarized properties of C-doped Mg3N2with C at two nonequivalent N sites. Results of our calculations reveal that the electronic properties are sensitive to the local structures and symmetries of doping sites while the magnetic moment is not. The substitution of C by N favors a spin-polarized state with a total magnetic moment of1.0μB per C, which is equal to the number of holes in the system. Our magnetic coupling calculations also indicate that substantial ferromagnetism is possible in the C-doped Mg3N2.
(3) The ferromagnetism and topological surface states manipulated by Mn in TI Bi2Te3are investigated. Our results indicate that substitution Mn for Bi can induce spin-polarized hole states with a total magnetic moments of4.0μB, and sufficient hole carrier density is required to obtain sustained magnetization. The obvious gap at the Dirac point coinciding with sharp surface state appears as Mn doped into Bi2Te3because the magnetic interactions break the time reversal symmetry.
(4) The manipulation effects by doping of2p light elements X (X=B, C, and N) on topological surface states in V2VI3(V=Bi and Sb, VI=Se and Te) are systemically explored. Our results unveil that X doping at anion sites can induce magnetic moments and gap opening at the Dirac point. To have a stable magnetic ground state, the dopant2p states must be sufficiently localized, which closely depends on the X-V bond lengths. In addition, the X-V bond length in X-doped V2VI3mainly depends on three factors:(1) the bonding environment of doping sites,(2) sizes of atoms, and (3) differences in their electronegativities.
(5) We explore the possibility of modifying the topological surface states and achieving the insulating massive Dirac fermion state in ternary TI Bi2Te2Se. Substitution of O for the outmost-layer Te leads to tunable surface states with an ideal Dirac cone. The co-substitution of Cr and O, as well as that of Mn and F, for the surface Bi and Te places the Dirac point inside the bulk band gap and opens a band gap at the Dirac point, hence creating the insulating massive Dirac fermion state.
(6) We theoretically reveal that co-substitution of magnetic and non-magnetic elements is a promising way to realize the insulating massive Dirac fermion state, and Fe is the best candidate to achieve it in Bi2Te3among M (M=Ti, V, Cr, Mn, and Fe). Substitution of M for Bi introduces perpendicular magnetism, but some energy bands cross the Fermi level. Furthermore, the synergistic effect of Fe and O places the Dirac point inside the bulk band gap and opens a surface band gap at the Dirac point with the Fermi level inside it.
(7) The occurrence of quantum anomalous Hall effect in ternary TIs TIBiTe2and T1BiSe2is predicted. The effective Hamiltonian analysis shows that the Hall conductance of the2D ferromagnetic TIs TF can be quantized. The first-principle calculations reveal that Cr is the best candidate to induce the ferromagnetic order in the insulating phase among X (X=Ti, Cr, Fe, and Au). The magnetic order in insulating phase arises from the spin polarization of substitutional Cr atoms and the free carriers are not needed for the formation of the substantial ferromagnetic coupling.
(8) Based on first-principles calculations and effective Hamiltonian analysis, we predict a topological phase transition from normal to topological insulators and the opening of a gap without breaking the time-reversal symmetry in TIBi(S1-xSex)2.The transition can be driven by modulating the Se concentration, and the rescaled spin-orbit coupling and lattice parameters are the key ingredients for the transition. For topological surface states, the Dirac cone evolves differently as the explicit breaking of inversion symmetry and the energy band gap can be opened under asymmetry surface. Our results present theoretical evidence for experimental observations [Science332,560(2011); Nat. Phys.7,840(2011)].
(9) We present theoretical evidence for modulating the topological surface states and achieving the insulating bulk states in solid-solution (Bi1-xSbx)2Te3. This is very important for applications of TIs in spintronics and quantum computation. Our results reveal that the band inversion occurs in (Bi1-xSbx)2Te3, indicating the non-triviality across the entire composition range, and the Dirac point moves upwards till it lies within the bulk energy gap accompanying the increase of Sb concentration x. In addition, with increasing x, the formation of prominent native defects becomes much more difficult, resulting in the truly insulating bulk.
(10) Here, using SnTe and PbTe as the examples, we give detailed insight into theeffects of SOC and strain on the formation of the topological crystalline insulator. A strain-induced band inversion, without any SOC, is shown. The SOC, however, is indispensable for achieving the topological crystalline insulator phase in real materials and can promote the process of the band inversion. Detailed surface state analysis reveals that topological surface state is thickness dependent and the Dirac point can locate precisely on or slightly away from the mirror-symmetry point. Our results pave a way of the material realization of new topological crystalline insulator.
The research results reveal the mechanism and effect rules of electronic structures, spin polarization, and related properties of doped TIs, provide the way of the surface gap opening and quantum anomalous Hall effect realization, and show the criteria of the material realization of new topological crystalline insulator. The studies pave the way to explore the fundamental physics phenomena and spintronic device applications of TIs, and are also helpful to discover the novel quantum states.
引文
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