拓扑物质中的量子霍尔效应研究

RESEARCH ON QUANTUM HALL EFFECTS IN TOPOLOGICAL MATTER

孙海鹏

11749311

博士

物理学

卢海舟

2021-05-21

2021-06-15

哈尔滨工业大学

深圳

量子霍尔效应最早是在强磁场下的二维电子气中观测到的，其量子霍尔电导可以表示为ne^2/h，其中𝑛为整数。这一结果开创了直接测量基本常数的新方法。随着研究的深入，人们发现量子霍尔电导中的整数𝑛可以表示为在布里渊区中所有占据态贝里曲率的积分，揭开了拓扑物质研究的序幕。拓扑物质是具有奇特拓扑性质的物态，其拓扑属性可以用拓扑不变量来刻画。由于拓扑物质其拓扑性质不受器件构型的影响，具有极大的应用前景，因此人们在不断寻找新的拓扑物质，研究其具有的独特拓扑性质。在量子反常霍尔效应发现以后，由于其无耗散边界态在制造低能耗电子器件方面具有巨大潜力，如何在拓扑物质中实现量子反常霍尔效应成为重要的研究方向。最近，有报道称MnBi2Te4为本征反铁磁拓扑绝缘体，理论计算显示其表面态具有88meV的能隙，并在其薄膜中观测到量子反常霍尔效应。然而最新的角分辨光电子能谱显示，其表面态有可能是无能隙的，这与之前的理论相差甚远。因此研究哪些因素会影响MnBi2Te4表面态的拓扑性质，以及如何进行量子反常霍尔效应调控不仅具有重要的理论价值，也有巨大的应用价值。此外，二维电子气在强磁场中会形成朗道能级，而朗道能级在样品边缘会发生形变与费米能相交，形成一维拓扑边缘态。拓扑边缘态以无损耗的方式运动，能够产生e^2/h整数倍的量子霍尔电导。然而在三维电子气中，沿磁场方向的维度阻止了霍尔电导的量子化。因此，研究三维拓扑材料中，要形成三维量子霍尔效应需要哪些条件，不仅在理解奇异拓扑物态方面有重要的理论价值，在物态调控方面也具有应用价值。综上所述，本文将研究如何在三维拓扑半金属中实现三维量子霍尔效应，以及研究影响MnBi2Te4表面态拓扑性质的因素和如何调控MnBi2Te4薄膜中的量子反常霍尔效应。主要的研究成果如下：我们研究了拓扑半金属在外加磁场中的三维量子霍尔效应。我们展示了在拓扑半金属中费米弧表面态通过外尔点可以产生独特的三维量子霍尔效应。由于存在拓扑约束，单个表面的费米弧是开放的，无法产生量子霍尔效应。在外尔点通过“虫洞”隧穿，上下两个表面的费米弧可以完成费米闭合回路产生量子霍尔效应。费米弧的边界态表现出特有的三维分布，可以看作（𝑑-2）维边界态的又一例证。此外，当费米面逐渐变化切过外尔点时，薄膜霍尔电导率由1/B依赖关系演变为量子化的平台。这一现象可以通过调节拓扑半金属平板的栅极电压来实现。我们还研究了最近新发现的本征反铁磁拓扑绝缘体MnBi2Te4表面态的拓扑性质。之前的理论预言MnBi2Te4中表面态会打开很大的能隙。然而最新的角分辨光电子能谱测量显示表面态的能隙不总是能观测到。为了解决这一理论预测与实验结果的分歧，我们从三维体哈密顿量出发，并考虑体磁化的空间分布，解析推导了半无穷结构单个表面的二维表面态有效模型。我们的计算结果显示，角分辨光电子能谱实验观测到的很小的表面态能隙可能是层内铁磁序变得更小和更局域造成的。此外，我们还计算了表面态的空间分布与穿透深度，计算表明表面态主要局域在样品表面的前两层七原层内。从我们的解析结果也可明确体参数对表面态的影响。同时，我们还推导了MnBi2Te4薄膜的表面态有效模型，展示了随厚度增加，有限尺寸效应减小。在样品较厚时，体磁化越局域，其有效磁化越小。我们还展示了陈数随奇偶层数变化在-1与0之间振荡。此外，我们研究了电场对本征反铁磁拓扑绝缘体MnBi2Te4薄膜中量子反常霍尔效应的调控。对于奇数层MnBi2Te4薄膜来说，如果电场诱导的势能𝑉足够大，其霍尔电导会由原来的e^2/h变为0，即陈数由1变为0。也就是说，随着𝑉的增大，发生了由拓扑非平庸态到拓扑平庸态的量子相变。此外，由于偶数层MnBi2Te4薄膜具有PT（空间反演-时间反演）对称性，能带的贝里曲率为零。但是，当在垂直于表面方向加电场时，会破坏系统的PT对称性，此时能带会破除简并，产生劈裂，能带的贝里曲率不再为零。因此，对于偶数层薄膜，当费米面切到能带时，外加电场会使偶数层薄膜的反常霍尔电导由0变为有限大小。但与奇数层不同的是，当费米能落在能隙中时，其霍尔电导依然为0，不随𝑉的改变而改变，即不会产生拓扑相变。

The quantum Hall effect was first observed in the two-dimensional electron gas under a strong magnetic field. The quantum Hall conductance can be expressed as ne^2/h, where 𝑛 is an integer. This result creates a new method of directly measuring fundamental constants. With the deepening of the research, it was discovered that the integer 𝑛 in quantum Hall conductance can be expressed as integrals of the Berry curvature of all occupied states in the Brillouin zone, which opened the prelude to the study of topological matter. Topological matter is a state of matter with exotic topological properties, and its topological properties can be described by topological invariants. Because the topological properties of topological matter are not affected by the geometry of the devices and have great application prospects, researchers are constantly searching for newtopological matter and studying their unique topological properties. After the discovery of the quantum anomalous Hall effect, because its non-dissipative boundary state has great potential in manufacturing low-energy electronic devices, how to realize the quantum anomalous Hall effect in topological materials has become an important research direction. Recently, it has been reported that MnBi2Te4 is an intrinsic antiferromagnetic topological insulator. Theoretical calculations show that its surface states have an energy gap of size 88 meV, and the quantum anomalous Hall effect has been observed in its thin film. However, the latest results of angle-resolved photoemission spectroscopy shows that the surface states may be gapless, which is far from the previous theory. Therefore, studying which factors will affect the topological properties of the surface states of MnBi2Te4 and how to adjust the quantum anomalous Hall effect has not only important theoretical value, but also huge application value. In addition, the two-dimensional electron gas will form Landau levels in a strong magnetic field, and the Landau levels will deform and intersect the Fermi energy at the edge of the sample, forming the one-dimensional topological edge states. The topological edge states move in a dissipationless manner and can generate quantum Hall conductance of integer multiples of e^2/h. However, in the three-dimensional electron gas, the dimension along the direction of the magnetic field prevents the quantization of Hall conductance. Therefore, in the study of three-dimensional topological materials, what conditions are needed to form a three-dimensional quantum Hall effect, not only have important value in understanding the unique topological state of matter, but also have application value in the aspect of control of quantum states. In summary, this dissertation will study how to realize the three-dimensional quantum Hall effect in three-dimensional topological semimetals, and the factors that affect the topological properties of MnBi2Te4 and how to control quantum anomalous Hall effect in MnBi2Te4 thin films. The main research results are as follows: We have studied the three-dimensional quantum Hall effect of topological semimetals in an external magnetic field. We show that the surface states of Fermi arcs in topological semimetals can produce a unique three-dimensional quantum Hall effect through theWeyl nodes. Due to the topological constraint, the Fermi arc on a single surface is open and cannot support the quantum Hall effect. The Fermi arcs on the upper and lower surfaces can complete the closed Fermi loop through the "wormhole" tunneling via Weyl nodes to produce the quantum Hall effect. The boundary states of the Fermi arc exhibit a unique three-dimensional distribution, which can be regarded as another example of the (𝑑-2)- dimensional boundary states. In addition, when the Fermi surface gradually changes and cuts through the Weyl node, the Hall conductivity of the film evolves from the 1/𝐵 dependence to a quantized platform. This phenomenon can be achieved by adjusting the gate voltage of the topological semimetal flake. We have also studied the topological properties of the surface states of the newly discovered intrinsic antiferromagnetic topological insulator MnBi2Te4. Previously, it was predicted that the surface states of MnBi2Te4 would open a large energy gap. However, the latest angle-resolved photoemission spectroscopy measurements show that the energy gap of the surface states is not always observable. In order to resolve this discrepancy between the theoretical prediction and experimental results, starting from the three-dimensional bulk Hamiltonian and considering the spatial distribution of bulk magnetization, we analytically deduce the two-dimensional effective model for the surface states of a single surface for a semi-infinite geometry. Our calculated results showthat the small surface gap observed in the angle-resolved photoemission spectroscopy experiments may be caused by a much smaller and more localized intralyer ferromagnetic order. In addition, we also calculate the spatial distribution and penetration depth of the surface states, which shows that the surface states are mainly localized in the first two septuple layers of the sample surface. From our analytical results, the influence of bulk parameters on surface states can be clarified. At the same time, we also deduce the effective model of the surface state for the MnBi2Te4 thin films, which shows that the finite size effect decreases as the thickness increases. When the sample is thicker, the more localized the bulk magnetization is, the smaller the effective magnetization wil be. We also show that the Chern number oscillates between -1 and 0 as the number of odd and even layers changes. In addition, we have studied the influence of the external electric field on the quantum anomalous Hall effect in the intrinsic antiferromagnetic topological insulator MnBi2Te4 thin films. For the odd-layer MnBi2Te4 thin film, if the potential energy 𝑉 induced by the electric field is large enough, the Hall conductance will change from the original e^2/h to 0, that is, the Chen number will change from 1 to 0. In other words, with the increase of 𝑉, a topological quantum phase transition from a topologically non-trivial state to a topologically trivial state occurs. In addition, because the even-layer MnBi2Te4 thin films has the PT (spatial inversion and time-reversal combined) symmetry, the Berry curvature of the energy band is zero. However, when an electric field is applied in the direction perpendicular to the surface, the PT symmetry of the system will be destroyed. At this time, the energy band will lift the degeneracy and split, and the Berry curvature of the energy band will no longer be zero. Therefore, for even-layer thin films, when the Fermi energy cuts to the energy band, the applied electric field will cause the anomalous Hall conductance of the even-layer thin films to change from zero to a finite value. Unlike the odd-layer thin films, when the Fermi energy falls in the surface gap, its Hall conductance is still 0, which does not change with the change of 𝑉, that is, no topological phase transition occurs.

拓扑绝缘体 磁性拓扑绝缘体 拓扑半金属 量子霍尔效应 量子反常霍尔效应

topological insulators magnetic topological insulators topological semimetals quantum Hall effect quantum anomalous Hall effect

中文

联合培养

南方科技大学

孙海鹏. 拓扑物质中的量子霍尔效应研究[D]. 深圳. 哈尔滨工业大学,2021.