Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. A new invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs.
Large anomalous Hall effect in ferromagnetic insulator-topological insulator heterostructures
我们证明了拓扑绝缘体化合物Bi 2 Te 3在铁磁绝缘体Cr 2 Ge 2 Te 6上的范德华外延。这些层的取向为Bi 2 Te 3的（001）平行于Cr2 Ge 2 Te 6的（001），Bi 2 Te 3的（110）平行于Cr2 Ge 2 Te 6的（100）。横截面透射电子显微镜表明形成了尖锐的界面。在低温下，由Bi_2 Te_3/Cr_2Ge_2 Te_6组成的双层膜表现出很大的反常霍尔效应（AHE）。倾斜场的AHE的研究表明，易轴位于沿c轴的异质结构，与体Cr2 Ge 2 Te 6的磁化测量一致。Cr2 Ge 2 Te 6的61 K居里温度和近化学计量比材料的使用可能导致基于AHE的自旋电子器件的发展。
We report a current scaling study of a quantum phase transition between a quantum anomalous Hall insulator and a trivial insulator on the surface of a heterostructure film of magnetic topological insulators. The transition was observed by tilting the magnetization while measuring the Hall conductivity $σ_{xy}$. The transition curves of $σ_{xy}$ taken under various excitation currents cross each other at a single point, exemplifying a quantum critical behavior of the transition. The slopes of the transition curves follow a power law dependence of the excitation current, giving a scaling exponen…
CrSb is an attractive material for room-temperature antiferromagnetic spintronic applications because of its high Néel temperature $\sim$700 K and semi-metallic character. We study the magnetic properties of CrSb bilayers on few-layer topological insulator thin films using \emph{ab initio} density functional theory. We find that the intrinsic parts of the total anomalous Hall conductivities of the thin films are non-zero, and approximately quantized. The Néel temperature of CrSb bilayers on few-layer topological insulator thin films is found to be approximately two times larger than that of an…
In two-dimensional anomalous Floquet insulators, non-Hermitian boundary state engineering can be used to completely separate chiral boundary states from bulk bands in the quasienergy spectrum. The topological properties of such spectrally separated boundary states are no longer restricted by the strict bulk-boundary correspondence of Hermitian systems. We show that this additional topological freedom enables one to faithfully transfer the topological properties of a boundary attached to a Floquet insulator to a non-Hermitian Floquet chain obtained by physically cutting off the boundary from th…
The search of novel topological phases, such as the quantum anomalous Hall insulator (QAHI) or the axion insulator, has motivated different schemes to introduce magnetism into topological insulators. One scheme is to introduce ferromagnetic dopants in topological insulators. However, it is generally challenging and requires carefully engineered growth/heterostructures or relatively low temperatures to observe the QAHI due to issues such as the added disorder with ferromagnetic dopants. Another promising scheme is using the magnetic proximity effect with a magnetic insulator to magnetize the to…
The phase transitions from one plateau to the next plateau or to an insulator in quantum Hall and quantum anomalous Hall (QAH) systems have revealed universal scaling behaviors. A magnetic-field-driven quantum phase transition from a QAH insulator to an axion insulator was recently demonstrated in magnetic topological insulator sandwich samples. Here, we show that the temperature dependence of the derivative of the longitudinal resistance on magnetic field at the transition point follows a characteristic power-law that indicates a universal scaling behavior for the QAH to axion insulator phase…
Anomalous and Topological Hall effect in Cu doped Sb2Te3 Topological Insulator
在不同温度和不同磁场下对Sb_（1.90）Cu_（0.10）Te_3的磁输运和磁化强度进行了测量。在高场下的磁输运测量表明体态和表面态共存。磁化强度显示了Cu掺杂诱导的反铁磁有序，观察到的量子振荡表明，在Sb 1.90 Cu 0.10 Te 3的磁化强度是体属性。霍尔数据的非线性表明存在反常和拓扑霍尔效应。根据Cu掺杂Sb_2Te_3拓扑绝缘体的霍尔测量数据，对反常和拓扑霍尔效应（THE）进行了评价.
Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
研究了拓扑绝缘体纳米线在沿其长度方向施加磁场时的输运性质。我们预测，与强表面无序，一个特征签名的带拓扑结构中透露的Aharonov玻姆（AB）振荡的电导。这些振荡具有异常周期$Φ_0=hc/e$的分量，并且在$\frac12Φ_0$的奇数倍处具有电导最大值，即当表面电子的AB相是$π$时。这与能带拓扑和表面曲率诱导的Berry相密切相关，特别是对于拓扑绝缘体表面。我们讨论了最近的实验上的Bi $_2$ Se $_3$纳米带的相似性和差异，并观察这种效果的最佳条件。
Chiral edge plasmons in quantum anomalous Hall insulators
Beijing Forestry University（北京林业大学）；Beijing Institute of Technology（北京理工大学）；Chinese Academy of Sciences（中国科学院）；University of Science and Technology of China（中国科学技术大学）
Anderson localization in two-dimensional topological insulators takes place via the so-called levitation and pair annihilation process. As disorder is increased, extended bulk states carrying opposite topological invariants move towards each other in energy, reducing the size of the topological gap, eventually meeting and localizing. This results in a topologically trivial Anderson insulator. Here, we introduce the anomalous levitation and pair annihilation, a process unique to periodically-driven, or Floquet systems. Due to the periodicity of the quasienergy spectrum, we find it is possible f…
Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
量子化版本的反常霍尔效应已被预测发生在磁性拓扑绝缘体中，但实验实现一直具有挑战性。本文报道了在磁性拓扑绝缘体Cr掺杂（Bi，Sb）2 Te 3薄膜中观察到的量子反常霍尔（QAH）效应。在零磁场下，门极调谐的反常霍尔电阻达到了预测的量子化值h/e^2，同时纵向电阻显著下降。在强磁场下，纵向电阻消失，而霍尔电阻保持在量子化值。QAH效应的实现可能导致低功耗电子器件的发展。
We uncover a new family of few-body topological phases in periodically driven fermionic systems in two dimensions. These phases, which we term correlation-induced anomalous Floquet insulators (CIAFIs), are characterized by quantized contributions to the bulk magnetization from multi-particle correlations, and are classified by a family of integer-valued topological invariants. The CIAFI phases do not require many-body localization, but arise in the generic situation of k-particle localization, where the system is localized (due to disorder) for any finite number of particles up to a maximum nu…
We theoretically show that the three-dimensional (3D) topological insulator (TI)/thin-film ferromagnetic metal (FMM) bilayer structure is possible to be a quantum anomalous Hall (QAH) insulator with a wide global band gap. Studying the band structure and the weight distributions of eigenstates, we demonstrate that the attachment of a metallic thin-film on the 3DTI can shift the topologically non-trivial state into the metal layers due to the hybridization of bands around the original Dirac point. By introducing the magnetic exchange interaction in the thin-film layers, we compute the anomalous…
The chiral hinge modes are the key feature of a second order topological insulator in three dimensions. Here we propose a quadrupole index in combination of a slab Chern number in the bulk to characterize the flowing pattern of chiral hinge modes along the hinges at the intersection of the surfaces of a sample. We further utilize the topological field theory to demonstrate the correspondent connection of the chiral hinge modes to the quadrupole index and the slab Chern number, and present a picture of three-dimensional quantum anomalous Hall effect as a consequence of chiral hinge modes. The t…
Giant Anisotropic Magnetoresistance in a Quantum Anomalous Hall Insulator
当三维（3D）铁磁拓扑绝缘体薄膜在面外磁化时，理想地通过无耗散的一维（1D）手征态发生传导，所述手征态的特征在于量子化的零场霍尔电导。最近实现的这种现象-量子反常霍尔效应-提供了一个概念上的新平台，研究边缘态传输，不同于更广泛研究的整数和分数量子霍尔效应，产生于朗道能级形成。在这种情况下出现了一个重要的问题：这些1D边缘状态如何演变的磁化从面外改变到面内？我们研究这个问题，通过研究场倾斜驱动的交叉从主要边缘状态的运输扩散运输在铬掺杂的（Bi，Sb）2 Te 3薄膜，作为系统从量子反常霍尔绝缘体过渡到一个无间隙，铁磁拓扑绝缘体。交叉体现在一个巨大的，电可调的各向异性磁阻，我们解释使用Landauer-Buttiker形式主义。我们的方法提供了一个强大的手段，量化边缘状态的贡献，运输温度和化学势制度远离完美的量化。
Shubnikov-de Haas oscillations in the anomalous Hall conductivity of Chern insulators
在蜂窝晶格上的霍尔模型是一个典型的例子，系统的特点是量子化霍尔电导率在没有外部磁场，即量子反常霍尔效应。最近的理论工作预测，在自旋轨道耦合较强的拓扑绝缘体和蜂窝层中，大质量狄拉克费米子的反常霍尔电导率可以表现出Shubnikov-de Haas（SdH）振荡。本文利用格点格林函数的精确谱展开，研究了强磁场作用下陈氏绝缘体的电子输运性质。我们发现，霍尔电导率的异常组件显示在低温下可见的SdH振荡。\textcolor{black}{The effect is shown to result from the modulation of the next-nearest neighbour flux accumulation due to the Haldane term,}，其从朗道光谱中去除电子-空穴对称性。为了支持我们的数值研究结果，我们推导出一个长波长的描述超出了线性（“狄拉克锥”）近似。最后讨论了反向磁场作用下能谱移动与拓扑能隙和晶格带宽的关系。
Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
量子反常霍尔绝缘体是一种二维绝缘态，在没有外加磁场的情况下，表现出与量子霍尔态相似的性质。它们具有量子化的霍尔电导$σ^H=Ce^2/h$，其中整数$C$被称为陈数，并且表示无间隙边缘模式的数量。最近的实验表明，掺铬薄膜（Bi，Sb）$_2$ Te $_3$是一种QAH绝缘体，具有陈数$C=\pm1$。在这里，我们从理论上预测，薄膜拓扑晶体绝缘体（TCI）可以托管各种QAH相，当掺杂铁磁有序掺杂剂。$\pm4$之间的任何陈氏数原则上可以作为（a）取决于磁掺杂浓度的感应塞曼场，（b）固有的或由压电材料通过邻近效应感应的结构变形，以及（c）薄膜的厚度之间的相互作用的结果而达到。在TCI中发现的可调陈氏数在超低功耗信息处理应用中具有重要的潜力。
After extensive investigation on the Floquet second-order topological insulator (FSOTI) in two dimension (2D), here we propose two driving schemes to systematically engineer the hierarchy of Floquet first-order topological insulator, FSOTI, and Floquet third-order topological insulator in three dimension (3D). Our driving protocols allow these Floquet phases to showcase regular $0$, anomalous $π$, and hybrid $0$-$π$-modes in a unified phase diagram, obtained for both 2D and 3D systems, while staring from the lower order topological or non-topological phases. Both the step drive and the mass ki…
Scattering of Electrons between Edge and Two-Dimensional States of a Two-Dimensional Topological Insulator and the Conductivity of the Topological Insulator Strip in a Metallic State
The anomalous Hall effect is caused by magnetic textures such as skyrmions. We derive an analytical formula of the Hall conductivity on the surface of a topological insulator up to third order in magnetization, $\boldsymbol{M}(\boldsymbol{x})$, based on a perturbative approach. We identify the magnetic textures that contribute to the Hall conductivity up to third order in magnetization and second order in spatial differentiation. We treat magnetization as a perturbation to calculate the Hall conductivity for each magnetic texture based on the linear response theory. Furthermore, we estimate th…
Large Anomalous Hall Effect in Topological Insulators with Proximitized Ferromagnetic Insulators
报道了由铁磁绝缘体Cr2 Ge 2 Te 6和拓扑绝缘体（Bi，Sb）2 Te 3组成的全碲化物异质结构中邻近驱动的大反常霍尔效应.尽管在（Bi，Sb）2 Te 3层的磁化小，异常霍尔电导率达到0.2e2/h的大值，符合铁磁响应的Cr2 Ge 2 Te 6。结果表明，拓扑绝缘体的表面态与邻近层Cr2 Ge 2 Te 6之间的交换耦合是有效的，并且足够强，可以打开表面态的交换能隙.
The nontrivial band topology can influence the Hofstadter spectrum. We investigate the Hofstadter spectrum for various models of Chern insulators under a rational flux $\frac{ϕ_{0}}{q}$, here $ϕ_{0}=\frac{h}{e}$ and $q$ being an integer. We find two major features. First, the number of splitting subbands is $|q-C|$ with Chern number $C$. Second, the anomalous open-orbit subbands with Chern numbers $q-1$ and $-q-1$ emerge, which are beyond the parameter window $(-q/2,q/2)$ of the Diophantine equation studied by Thouless-Kohmoto-Nightingale-den Nijs [Phys. Rev. Lett. \textbf{49}, 405 (1982)]. Th…
Eigenenergies of a non-Hermitian system without parity-time symmetry are complex in general. Here, we show that the chiral boundary states of higher-dimensional (two-dimensional and three-dimensional) non-Hermitian topological insulators without parity-time symmetry can be Hermitian with real eigenenergies under certain conditions. Our approach allows one to construct Hermitian chiral edge and hinge states from non-Hermitian two-dimensional Chern insulators and three-dimensional second-order topological insulators, respectively. Such Hermitian chiral boundary channels have perfect transmission…
Doping a topological insulator (TI) film with transition metal ions can break its time-reversal symmetry and lead to the realization of the quantum anomalous Hall (QAH) effect. Prior studies have shown that the longitudinal resistance of the QAH samples usually does not vanish when the Hall resistance shows a good quantization. This has been interpreted as a result of the presence of possible dissipative conducting channels in magnetic TI samples. By studying the temperature- and magnetic field-dependence of the magnetoresistance of a magnetic TI sandwich heterostructure device, we demonstrate…
Recently, the magnetic topological insulator MnBi$_2$Te$_4$ emerged as a competitive platform to realize quantum anomalous Hall (QAH) states. We report a Berry-curvature splitting mechanism to realize the QAH effect in the disordered magnetic TI multilayers when switching from an antiferromagnetic order to a ferromagnetic order. We reveal that the splitting of spin-resolved Berry curvature, originating from the separation of the mobility edge during the magnetic switching, can give rise to a QAH insulator even \emph{without} closing the band gap. We present a global phase diagram, and also pro…
Lecture-notes: introducing and discussing basics on axion electrodynamics with application in the calculation of the images generated by an electric (or a magnetic) charge located close to an interface ordinary insulator-topological insulator
We study spin conductivity of the surface states in a thin film of a topological insulator with Kubo formulas. Hybridization between the different sides of the film opens a gap at the Dirac point. We found that in the gapped region spin conductivity remains finite. In the gapless region near the band gap spin conductivity is enhanced. These findings make a thin film of a topological insulator as a promising material for spintronic applications.
