磁场与磁性调控的拓扑材料输运性质研究

  拓扑物理是本世纪以来凝聚态物理学研究中取得的最大的进展之一。拓扑概念的引入使得人们对物相的分类和认知提升了一个新的台阶。从拓扑概念中衍生出来的第一个拓扑材料即为拓扑绝缘体，它也是拓扑材料中最具代表性的一个。拓扑绝缘体内部的能带结构与外界拓扑不同，因此拓扑相变发生在其界面处，这使其在界面拥有了稳定的界面态。这种拓扑保护的界面态是拓扑材料最广为人知的特性。在拓扑绝缘体发现之后，狄拉克半金属、外尔半金属、节线半金属等拓扑材料被陆续提出并一一实验实现。近年来，研究者开始研究磁性拓扑材料和高阶拓扑材料，并在光学、声学、电路等经典系统中自主设计和制造拓扑系统。因其与传统材料拓扑不同的能带结构，拓扑材料往往展现出各种新奇的物理性质。这使它们成为了研究新一类输运现象的绝佳平台。本论文将具体从以下几个方面研究拓扑材料中的输运特性。

  从量子理论出发，我们研究了多个低能有效模型中各个方向的磁电阻，并考虑了不同杂质势能的影响。通过对磁电阻的解析推导和计算，我们得到了两个重要的结果：第一，在拥有单个狄拉克锥型能带结构的材料中量子极限下的纵向磁电阻反比于磁场强度且不受杂质散射的影响；第二，量子极限下的线性磁电阻并非拥有线性能谱的系统所独有，其同样存在于拥有二次方型能谱的系统中。此外，计算表明长程高斯势能型杂质可以同时带来线性的纵向和横向磁电阻，而屏蔽库伦势能型杂质只能导致线性的横向磁电阻。以上这些结果给出了准一维朗道能带系统中杂质散射的机制和物理意义，并解释了实验上观测到的线性纵向磁电阻。本文中对磁电阻的研究给拓扑半金属的输运性质带来了新的见解，并推动了线性磁电阻方向的研究进展。

  我们发展了磁场中电荷密度波的理论框架，并通过计算发现在ZrTe₅中电子和声子之间的相互作用是形成电荷密度波的关键，而费米波矢固定的公度电荷密度波支持了ZrTe₅中的量子霍尔平台。这种电荷密度波机制的三维量子霍尔效应的独特之处在于磁场强度同时调控了系统在沿磁场方向发生的序参数相变和在垂直于磁场方向的平面内发生的拓扑相变。本文中的理论分析和计算结果解释了实验在ZrTe₅中观测到的三维量子霍尔效应，有助于将无耗散输运早日投入到实际应用中。

  我们提出了通过非局域化测量来区分轴子绝缘体和普通绝缘体的方法，并对比研究了理想轴子绝缘体和反铁磁拓扑绝缘体MnBi₂Te₄的非局域化电阻值。数值计算表明MnBi₂Te₄中存在着未量子化的非局域化输运现象，并且其非局域化电阻对费米能量变化、杂质和电极厚度的影响有一定的抵抗力。此外，本论文还发现了奇数层和偶数层的MnBi₂Te₄器件可以通过不同测量方式下得到的非局域化电阻值加以区分。这些结果为实验上测量MnBi₂Te₄的非局域化输运以及寻找轴子绝缘体提供了切实可行的方案。

  Topological physics is one of the greatest advancements made in the study of condensed matter physics since this century. The introduction of topology concepts has taken the classification and understanding of matter to a new level. The first topological material derived from the concept of topology is the topological insulator, which is also the most representative one among topological materials. The bulk energy band structure of topological insulators is topologically different from that of the outside; therefore, the topological transition happens at the interface, giving the topological insulator stable interface states. The topologically protected interface states are the most known feature of the topological materials. After the discovery of topological insulators, many other topological materials have been proposed and experimentally realized, including Dirac semimetals, Weyl semimetals, nodal-line semimetals, and so on. In recent years, researchers have started to investigate magnetic topological materials and higher-order topological materials, and design and manufacture topological systems in classical systems such as optical systems, acoustic systems, and electric circuits. Because their energy band structures are topologically different from those of traditional materials, topological materials often exhibit various novel physical properties. This makes them the ideal platform for investigating a new class of transport phenomena. This dissertation will study the transport properties of topological materials from the following aspects.

  Starting from the quantum theory, we have studied the magnetoresistance in various directions in several low-energy effective models, and the effect of different types of impurities has been considered. By the analytical derivation and calculations of the magnetoresistance, we have obtained two important results: first, the longitudinal magnetoresistance in the quantum limit is inversely proportional to the magnetic field strength, independent of impurity scattering, in materials with a single Dirac cone dispersion; second, linear magnetoresistance in the quantum limit is not exclusive to systems with linear energy dispersion, but can also occur in systems with quadratic energy dispersion. In addition, calculations show that the long-range Gaussian-type impurity can induce both linear longitudinal and transverse magnetoresistance, but the screened-Coulomb-type impurity can only induce linear transverse magnetoresistance. The above results reveal the scattering mechanisms and the corresponding physical meaning in the quasi-one-dimensional systems with Landau bands, and explain the linear longitudinal magnetoresistance observed in experiments. The investigation of magnetoresistance in this dissertation brings new insights into the transport properties of topological semimetals and advances research progress in the field of linear magnetoresistance.

  We have developed the theory of the charge density wave under the magnetic field. Calculations show that the electron-phonon interactions in ZrTe₅ are responsible for the form of the charge density wave, and the three-dimensional quantum Hall effect of ZrTe₅ is supported by a fixed-Fermi-wavevector commensurate charge density wave. The three-dimensional quantum Hall effect supported by the charge density wave is special in that the magnetic field strength simultaneously governs the order parameter phase transition of the system along the magnetic field direction and the topological phase transition perpendicular to the magnetic field direction. Theoretical analysis and calculations in this dissertation can explain the three-dimensional quantum Hall effect observed in ZrTe₅ and help to further promote the dissipationless transport into practical applications.

  We have proposed using the nonlocal measurement to distinguish the axion insulators and normal insulators, and comparatively investigated the nonlocal resistance in the ideal axion insulator and the antiferromagnetic MnBi₂Te₄. Numerical calculations show that there exists non-quantized nonlocal transport in MnBi₂Te₄, which is robust against Fermi energy change, impurities, and electrode thickness. Additionally, this dissertation discovers that MnBi₂Te₄ devices of even-number-layer and odd-number-layer can be distinguished based on the nonlocal resistance measured in different ways. The above results provide a practical approach to measuring the nonlocal transport of MnBi₂Te₄ in experiments and search for axion insulators.

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