High-Chern-number and high-temperature quantum Hall effect without Landau levels

Novel /2-Periodic Planar Hall Effect Due to Orbital Magnetic Moments in MnBi2Te4

The Berry curvature and orbital magnetic moment (OMM) come from either inversion symmetry or time-reversal symmetry breaking in quantum materials. Here, we demonstrate the significance of OMMs and Berry curvature in planar Hall effect (PHE) in antiferromagnetic topological insulator MnBi₂Te₄ flakes. We observe a PHE with period of π and positive magnitude at low fields, resembling the PHE of the surface states in nonmagnetic topological insulators. Remarkably, a novel predominant PHE with period of π/2 and negative magnitude emerges below the Néel temperature with B > 10 T. Our theoretical calculations reveal that this unusual π/2-periodic PHE originates from the topological OMMs of bulk Dirac electrons. Moreover, the competition between the contributions from the bulk and the surface states leads to nontrivial evolutions of PHE and anisotropic magnetoresistance. Our results reveal intriguing electromagnetic response due to the OMMs and also provide insight into the potential applications of magnetic topological insulators in spintronics.

Layer-Number-Dependent Antiferromagnetic and Ferromagnetic Behavior in MnSb_{2}Te_{4}

MnBi_{2}Te_{4}, an intrinsic magnetic topological insulator, has shown layer-number-correlated magnetic and topological phases. More interestingly, in the isostructural material MnSb_{2}Te_{4}, the antiferromagnetic (AFM) and ferromagnetic (FM) states have been both observed in the bulk counterparts, which are also predicted to be topologically nontrivial. Revealing the layer-number-dependent magnetic properties of MnSb_{2}Te_{4} down to a single septuple layer (SL) is of great significance for exploring the topological phenomena. However, this is still elusive. Here, using the polar reflective magnetic circular dichroism spectroscopy, both the A-type AFM and FM behaviors are observed and comprehensively studied in MnSb_{2}Te_{4} down to a single SL limit. In A-type AFM MnSb_{2}Te_{4} flakes, an obvious odd-even layer-number effect is observed. An additional surface spin-flop (SSF) transition occurs in even-SL flakes with the number of layers larger than 2. With the AFM linear-chain model, we identify that the even-SL flakes stabilize in a collinear state between the SSF transition and the spin-flop transition due to their appropriate energy ratio between the magnetic-field-scale anisotropy and interlayer interaction. In FM MnSb_{2}Te_{4} flakes, we observe very different magnetic behaviors with an abrupt spin-flipping transition and very small saturation fields, indicating a weakened interlayer interaction. By revealing the rich magnetic states of few-SL MnSb_{2}Te_{4} on the parameter space of the number of layers, external magnetic field, and temperature, our findings pave the way for further quantum transport studies of few-SL MnSb_{2}Te_{4}.

Chiral Majorana edge modes and vortex Majorana zero modes in superconducting antiferromagnetic topological insulator

The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetryTc. In this paper we investigate the effects of thes-wave superconducting pairings on the multilayers of AFTI, which breaksTcsymmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern numberC= ±2. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}

In most cases, to observe quantized Hall plateaus, an external magnetic field is applied in intrinsic magnetic topological insulators MnBi_{2}Te_{4}. Nevertheless, whether the nonzero Chern number (C≠0) phase is a quantum anomalous Hall (QAH) state, or a quantum Hall (QH) state, or a mixing state of both is still a puzzle, especially for the recently observed C=2 phase [Deng et al., Science 367, 895 (2020)SCIEAS0036-807510.1126/science.aax8156]. In this Letter, we propose a physical picture based on the Anderson localization to understand the observed Hall plateaus in disordered MnBi_{2}Te_{4}. Rather good consistency between the experimental and numerical results confirms that the bulk states are localized in the absence of a magnetic field and a QAH edge state emerges with C=1. However, under a strong magnetic field, the lowest Landau band formed with the localized bulk states, survives disorder, together with the QAH edge state, leading to a C=2 phase. Eventually, we present a phase diagram of a disordered MnBi_{2}Te_{4} which indicates more coexistence states of QAH and QH to be verified by future experiments.

Intrinsic Magnetic Topological Insulator State Induced by the Jahn-Teller Effect

The Jahn-Teller effect is a geometrical distortion which lowers the system symmetry and lifts orbital degeneracy in molecules and solids. It affects a wide range of properties, including magnetic and band structures. In this work we propose a family of Cr-containing intrinsic magnetic topological insulator materials which are subjected to a pseudo-Jahn-Teller effect-CrBi₂Se₄, CrBi₂Te₂Se₂, and CrBi₂Te₄. Using first-principles calculations we study their properties and investigate the impact of Jahn-Teller distortions on the electronic and magnetic properties. We show that these distortions can significantly affect magnetic anisotropy energy and band structure. Without the distortions accounted for, all three of the compounds exhibit a semimetallic band structure. The distortions open a band gap, which in the cases of CrBi₂Te₂Se₂ and CrBi₂Te₄ is inverted. We also investigate the CrBi₂Te₂Se₂ and CrBi₂Te₄ surface band structure and demonstrate that the surface states have a topological origin.

Even-Odd Layer-Dependent Anomalous Hall Effect in Topological Magnet MnBi2Te4 Thin Films

Recently, MnBi₂Te₄ has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi₂Te₄ flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi₂Te₄ films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi₂Te₄ phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi₂Te₃ phase. The extracted AH component of the MnBi₂Te₄ phase shows a clear even-odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi₂Te₄ films.

Quantum anomalous Hall effect in Cr2Ge2Te6/Bi2Se3/Cr2Ge2Te6heterostructures

Currently, quantum anomalous Hall (QAH) effect can only be observed at very low temperatures, which severely hinders its utilization from spintronics to quantum computation. Finding or predicting new systems supporting QAH effect at high temperatures remains essential and challenging. This work presents first-principles studies on the proximity effect between Bi₂Se₃slabs and Cr₂Ge₂Te₆(CGT) layers, reporting that Chern insulators are available in CGT/Bi₂Se₃/CGT heterostructures. If the sandwiched Bi₂Se₃slab is 4 quintuple layers (QLs) or thicker, the Chern insulating state is robust against the interfacial stacking manner. If the Bi₂Se₃slab is only 2 or 3 QLs, the CrBi- and CrH-aligned heterostructures are also Chern insulators, while the CrSe-aligned ones are trivial. The Chern insulators support the Hall conductivityσ_xy=e²/hand have energy gaps ranging from 3 to 20 meV, implying QAH effect at higher temperatures. An effective model Hamiltonian is introduced to understand the topological phase of the heterostructures.

Large Anomalous Hall and Nernst Effects in High Curie-Temperature Iron-Based Heusler Compounds

The interplay between topology and magnetism has recently sparked the frontier studies of magnetic topological materials that exhibit intriguing anomalous Hall and Nernst effects owning to the large intrinsic Berry curvature (BC). To better understand the anomalous quantum transport properties of these materials and their implications for future applications such as electronic and thermoelectric devices, it is crucial to discover more novel material platforms for performing anomalous transverse transport studies. Here, it is experimentally demonstrated that low-cost Fe-based Heusler compounds exhibit large anomalous Hall and Nernst effects. An anomalous Hall conductivity of 250-750 S cm-1 and Nernst thermopower of above 2 µV K-1 are observed near room temperature. The positive effect of anti-site disorder on the anomalous Hall transport is revealed. Considering the very high Curie temperature (nearly 1000 K), larger Nernst thermopowers at high temperatures are expected owing to the existing magnetic order and the intrinsic BC. This work provides a background for developing low-cost Fe-based Heusler compounds as a new material platform for anomalous transport studies and applications, in particular, near and above room temperature.

Ferromagnetism of two-dimensional transition metal chalcogenides: both theoretical and experimental investigations

In recent years, with the fast development of integrated circuit electronic devices and technologies, it has become urgent to improve the density of data storage and lower the energy losses of devices. Under these circumstances, two-dimensional (2D) materials, which have a smaller size and lower energy loss compared with bulk materials, are becoming ideal candidates for future spintronic devices. Among them, 2D transition metal chalcogenides (TMCs), which have excellent electronic and optical properties, have attracted great attention from researchers. However, most of them are intrinsically non-magnetic, which severely hinders their further applications in spintronics. Therefore, introducing intrinsic room-temperature ferromagnetism into 2D TMC materials has become an important issue in spintronics. In this work, we review the introduction of intrinsic ferromagnetism into typical 2D TMCs using various strategies, such as defect engineering, doping with transition metal elements, and phase transfer. Additionally, we found that their ferromagnetism could be adjusted via changing the experimental conditions, such as the nucleation temperature, ion irradiation dose, doping amount, and phase ratio. Finally, we provide some insight into prospective solutions for introducing ferromagnetism into 2D TMCs, hoping to shed some light on future spintronics development.

Magnetic-field-induced robust zero Hall plateau state in MnBi2Te4 Chern insulator

The intrinsic antiferromagnetic topological insulator MnBi2Te4 provides an ideal platform for exploring exotic topological quantum phenomena. Recently, the Chern insulator and axion insulator phases have been realized in few-layer MnBi2Te4 devices at low magnetic field regime. However, the fate of MnBi2Te4 in high magnetic field has never been explored in experiment. In this work, we report transport studies of exfoliated MnBi2Te4 flakes in pulsed magnetic fields up to 61.5 T. In the high-field limit, the Chern insulator phase with Chern number C = -1 evolves into a robust zero Hall resistance plateau state. Nonlocal transport measurements and theoretical calculations demonstrate that the charge transport in the zero Hall plateau state is conducted by two counter-propagating edge states that arise from the combined effects of Landau levels and large Zeeman effect in strong magnetic fields. Our result demonstrates the intricate interplay among intrinsic magnetic order, external magnetic field, and nontrivial band topology in MnBi2Te4.

Light-Tunable Surface State and Hybridization Gap in Magnetic Topological Insulator MnBi8Te13

MnBi₈Te₁₃ is an intrinsic ferromagnetic (FM) topological insulator with different complex surface terminations. Resolving the electronic structures of different termination surfaces and manipulation of the electronic state are important. Here, by using micrometer spot time- and angle-resolved photoemission spectroscopy (μ-TrARPES), we resolve the electronic structures and reveal the ultrafast dynamics upon photoexcitation. Photoinduced filling of the surface state hybridization gap is observed for the Bi₂Te₃ quintuple layer directly above MnBi₂Te₄ accompanied by a nontrivial shift of the surface state, suggesting light-tunable interlayer interaction. Relaxation of photoexcited electrons and holes is observed within 1-2 ps. Our work reveals photoexcitation as a potential control knob for tailoring the interlayer interaction and surface state of MnBi₈Te₁₃.

Electron-Phonon and Spin-Lattice Coupling in Atomically Thin Layers of MnBi2Te4

MnBi₂Te₄ represents a new class of magnetic topological insulators in which novel quantum phases emerge at temperatures higher than those found in magnetically doped thin films. Here, we investigate how couplings between electron, spin, and lattice are manifested in the phonon spectra of few-septuple-layer thick MnBi₂Te₄. After categorizing phonon modes by their symmetries, we study the systematic changes in frequency, line width, and line shape of a spectrally isolated A_1g mode. The electron-phonon coupling increases in thinner flakes as manifested in a broader phonon line width, which is likely due to changes of the electron density of states. In 4- and 5-septuple thick samples, the onset of magnetic order below the Néel temperature is concurrent with a transition to an insulating state. We observe signatures of a reduced electron-phonon scattering across this transition as reflected in the reduced Fano parameter. Finally, spin-lattice coupling is measured and modeled from temperature-dependent phonon frequency.

Layer Hall effect in a 2D topological axion antiferromagnet

Whereas ferromagnets have been known and used for millennia, antiferromagnets were only discovered in the 1930s¹. At large scale, because of the absence of global magnetization, antiferromagnets may seem to behave like any non-magnetic material. At the microscopic level, however, the opposite alignment of spins forms a rich internal structure. In topological antiferromagnets, this internal structure leads to the possibility that the property known as the Berry phase can acquire distinct spatial textures^2,3. Here we study this possibility in an antiferromagnetic axion insulator-even-layered, two-dimensional MnBi₂Te₄-in which spatial degrees of freedom correspond to different layers. We observe a type of Hall effect-the layer Hall effect-in which electrons from the top and bottom layers spontaneously deflect in opposite directions. Specifically, under zero electric field, even-layered MnBi₂Te₄ shows no anomalous Hall effect. However, applying an electric field leads to the emergence of a large, layer-polarized anomalous Hall effect of about 0.5e²/h (where e is the electron charge and h is Planck's constant). This layer Hall effect uncovers an unusual layer-locked Berry curvature, which serves to characterize the axion insulator state. Moreover, we find that the layer-locked Berry curvature can be manipulated by the axion field formed from the dot product of the electric and magnetic field vectors. Our results offer new pathways to detect and manipulate the internal spatial structure of fully compensated topological antiferromagnets^4-9. The layer-locked Berry curvature represents a first step towards spatial engineering of the Berry phase through effects such as layer-specific moiré potential.

Pressure-Tuned Intralayer Exchange in Superlattice-Like MnBi2Te4/(Bi2Te3)n Topological Insulators

The magnetic structures of MnBi₂Te₄(Bi₂Te₃)_n can be manipulated by tuning the interlayer coupling via the number of Bi₂Te₃ spacer layers n, while the intralayer ferromagnetic (FM) exchange coupling is considered too robust to control. By applying hydrostatic pressure up to 3.5 GPa, we discover opposite responses of magnetic properties for n = 1 and 2. MnBi₄Te₇ stays at A-type antiferromagnetic (AFM) phase with a decreasing Néel temperature and an increasing saturation field. In sharp contrast, MnBi₆Te₁₀ experiences a phase transition from A-type AFM to a quasi-two-dimensional FM state with a suppressed saturation field under pressure. First-principles calculations reveal the essential role of intralayer exchange coupling from lattice compression in determining these magnetic properties. Such magnetic phase transition is also observed in 20% Sb-doped MnBi₆Te₁₀ because of the in-plane lattice compression.

P-orbital magnetic topological states on square lattice

Honeycomb or triangular lattices were extensively studied and thought to be proper platforms for realizing the quantum anomalous Hall effect (QAHE), where magnetism is usually caused by d orbitals of transition metals. Here we propose that a square lattice can host three magnetic topological states, including the fully spin-polarized nodal loop semimetal, QAHE and the topologically trivial ferromagnetic semiconductor, in terms of the symmetry and k · p model analyses that are material independent. A phase diagram is presented. We further show that the above three magnetic topological states can indeed be implemented in the two-dimensional (2D) materials ScLiCl₅, LiScZ₅ (Z=Cl, Br) and ScLiBr₅, respectively. The ferromagnetism in these 2D materials is microscopically revealed from p electrons of halogen atoms. This present study opens a door to explore the exotic topological states as well as quantum magnetism from p-orbital electrons by means of the material-independent approach.

Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators

The topological surface states of magnetic topological systems, such as Weyl semimetals and axion insulators, are associated with unconventional transport properties such as nonzero or half-quantized surface anomalous Hall effect. Here we study the surface anomalous Hall effect and its spectral signatures in different magnetic topological phases using both model Hamiltonian and first-principles calculations. We demonstrate that by tailoring the magnetization and interlayer electron hopping, a rich three-dimensional topological phase diagram can be established, including three types of topologically distinct insulating phases bridged by Weyl semimetals, and can be directly mapped to realistic materials such as MnBi2Te4/(Bi2Te3)n systems. Among them, we find that the surface anomalous Hall conductivity in the axion-insulator phase is a well-localized quantity either saturated at or oscillating around e2/2h, depending on the magnetic homogeneity. We also discuss the resultant chiral hinge modes embedded inside the side surface bands as the potential experimental signatures for transport measurements. Our study is a significant step forward towards the direct realization of the long-sought axion insulators in realistic material systems.

Intrinsic magnetic topological insulators

Introducing magnetism into topological insulators breaks time-reversal symmetry, and the magnetic exchange interaction can open a gap in the otherwise gapless topological surface states. This allows various novel topological quantum states to be generated, including the quantum anomalous Hall effect (QAHE) and axion insulator states. Magnetic doping and magnetic proximity are viewed as being useful means of exploring the interaction between topology and magnetism. However, the inhomogeneity of magnetic doping leads to complicated magnetic ordering and small exchange gaps, and consequently the observed QAHE appears only at ultralow temperatures. Therefore, intrinsic magnetic topological insulators are highly desired for increasing the QAHE working temperature and for investigating topological quantum phenomena further. The realization and characterization of such systems are essential for both fundamental physics and potential technical revolutions. This review summarizes recent research progress in intrinsic magnetic topological insulators, focusing mainly on the antiferromagnetic topological insulator MnBi2Te4 and its family of materials.

Topological Magnetic Materials of the (MnSb2Te4)·(Sb2Te3)n van der Waals Compounds Family

Using density functional theory, we propose the (MnSb₂Te₄)·(Sb₂Te₃)_n family of stoichiometric van der Waals compounds that harbor multiple topologically nontrivial magnetic phases. In the ground state, the first three members of the family (n = 0, 1, 2) are 3D antiferromagnetic topological insulators, while for n ≥ 3 a special phase is formed, in which a nontrivial topological order coexists with a partial magnetic disorder in the system of the decoupled 2D ferromagnets, whose magnetizations point randomly along the third direction. Furthermore, due to a weak interlayer exchange coupling, these materials can be field-driven into the FM Weyl semimetal (n = 0) or FM axion insulator states (n ≥ 1). Finally, in two dimensions, we reveal these systems to show intrinsic quantum anomalous Hall and AFM axion insulator states, as well as quantum Hall state, achieved under external magnetic field. Our results demonstrate that MnSb₂Te₄ is not topologically trivial as was previously believed that opens possibilities of realization of a wealth of topologically nontrivial states in the (MnSb₂Te₄)·(Sb₂Te₃)_n family.

Critical Behavior and Universal Signature of an Axion Insulator State

Recently, the search for an axion insulator state in the ferromagnetic-3D topological insulator (TI) heterostructure and MnBi_{2}Te_{4} has attracted intense interest. However, its detection remains difficult in experiments. We systematically investigate the disorder-induced phase transition of the axion insulator state in a 3D TI with antiparallel magnetization alignment surfaces. It is found that there exists a 2D disorder-induced phase transition on the surfaces of the 3D TI which shares the same universality class with the quantum Hall plateau to plateau transition. Then, we provide a phenomenological theory which maps the random mass Dirac Hamiltonian of the axion insulator state into the Chalker-Coddington network model. Therefore, we propose probing the axion insulator state by investigating the universal signature of such a phase transition in the ferromagnetic-3D TI heterostructure and MnBi_{2}Te_{4}. Our findings not only show a global phase diagram of the axion insulator state, but also stimulate further experiments to probe it.

Intertwined Topological and Magnetic Orders in Atomically Thin Chern Insulator MnBi2Te4

MnBi₂Te₄, a van der Waals magnet, is an emergent platform for exploring Chern insulator physics. Its layered antiferromagnetic order was predicted to enable even-odd layer number dependent topological states. Furthermore, it becomes a Chern insulator when all spins are aligned by an applied magnetic field. However, the evolution of the bulk electronic structure as the magnetic state is continuously tuned and its dependence on layer number remains unexplored. Here, employing multimodal probes, we establish one-to-one correspondence between bulk electronic structure, magnetic state, topological order, and layer thickness in atomically thin MnBi₂Te₄ devices. As the magnetic state is tuned through the canted magnetic phase, we observe a band crossing, i.e., the closing and reopening of the bulk band gap, corresponding to the concurrent topological phase transition in both even- and odd-layer-number devices. Our findings shed new light on the interplay between band topology and magnetic order in this newly discovered topological magnet.

Two-dimensional magnetic materials: structures, properties and external controls

Since the discovery of intrinsic ferromagnetism in atomically thin Cr2Gr2Te6 and CrI3 in 2017, research on two-dimensional (2D) magnetic materials has become a highlighted topic. Based on 2D magnetic materials and their heterostructures, exotic physical phenomena at the atomically thin limit have been discovered, such as the quantum anomalous Hall effect, magneto-electric multiferroics, and magnon valleytronics. Furthermore, magnetism in these ultrathin magnets can be effectively controlled by external perturbations, such as electric field, strain, doping, chemical functionalization, and stacking engineering. These attributes make 2D magnets ideal platforms for fundamental research and promising candidates for various spintronic applications. This review aims at providing an overview of the structures, properties, and external controls of 2D magnets, as well as the challenges and potential opportunities in this field.

Spin Fluctuations in Quantized Transport of Magnetic Topological Insulators

In magnetic topological insulators, quantized electronic transport is intertwined with spontaneous magnetic ordering, as magnetization controls band gaps, hence band topology, through the exchange interaction. We show that considering the exchange gaps at the mean-field level is inadequate to predict phase transitions between electronic states of distinct topology. Thermal spin fluctuations disturbing the magnetization can act as frozen disorders that strongly scatter electrons, reducing the onset temperature of quantized transport appreciably even in the absence of structural impurities. This effect, which has hitherto been overlooked, provides an alternative explanation of recent experiments on magnetic topological insulators.

Six-membered-ring inorganic materials: definition and prospects

The six-membered ring (SMR) is a common structure unit for numerous material systems. These materials include, but are not limited to, the typical two-dimensional materials such as graphene, h-BN, and transition metal dichalcogenides, as well as three-dimensional materials such as beryllium, magnesium, MgB2 and Bi2Se3. Although many of these materials have already become 'stars' in materials science and condensed-matter physics, little attention has been paid to the roles of the SMR unit across a wide range of compositions and structures. In this article, we systematically analyze these materials with respect to their very basic SMR structural unit, which has been found to play a deterministic role in the occurrence of many intriguing properties and phenomena, such as Dirac electronic and phononic spectra, superconductivity and topology. As a result, we have defined this group of materials as SMR inorganic materials, opening up a new perspective on materials research and development. With their unique properties, SMR materials deserve wide attention and in-depth investigation from materials design, new physical discoveries to target-wizard applications. It is expected that SMR materials will find niche applications in next-generation information technology, renewable energy, space, etc.

Persistent surface states with diminishing gap in MnBi2Te4/Bi2Te3 superlattice antiferromagnetic topological insulator

Magnetic topological quantum materials (TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic (AFM) topological insulator MnBi₂Te₄ that could realize quantized anomalous Hall effect and axion insulator phase ignited intensive study on this family of TQM compounds. Here, we investigated the AFM compound MnBi₄Te₇ where Bi₂Te₃ and MnBi₂Te₄ layers alternate to form a superlattice. Using spatial- and angle-resolved photoemission spectroscopy, we identified ubiquitous (albeit termination dependent) topological electronic structures from both Bi₂Te₃ and MnBi₂Te₄ terminations. Unexpectedly, while the bulk bands show strong temperature dependence correlated with the AFM transition, the topological surface states with a diminishing gap show negligible temperature dependence across the AFM transition. Together with the results of its sister compound MnBi₂Te₄, we illustrate important aspects of electronic structures and the effect of magnetic ordering in this family of magnetic TQMs.

Tuning the Chern number in quantum anomalous Hall insulators

A quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has a quantized Hall resistance of h/(Ce²) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an integer)^1,2. The QAH effect has been realized in magnetic topological insulators^3-9 and magic-angle twisted bilayer graphene^10,11. However, the QAH effect at zero magnetic field has so far been realized only for C = 1. Here we realize a well quantized QAH effect with tunable Chern number (up to C = 5) in multilayer structures consisting of alternating magnetic and undoped topological insulator layers, fabricated using molecular beam epitaxy. The Chern number of these QAH insulators is determined by the number of undoped topological insulator layers in the multilayer structure. Moreover, we demonstrate that the Chern number of a given multilayer structure can be tuned by varying either the magnetic doping concentration in the magnetic topological insulator layers or the thickness of the interior magnetic topological insulator layer. We develop a theoretical model to explain our experimental observations and establish phase diagrams for QAH insulators with high, tunable Chern number. The realization of such insulators facilitates the application of dissipationless chiral edge currents in energy-efficient electronic devices, and opens up opportunities for developing multi-channel quantum computing and higher-capacity chiral circuit interconnects.

Emergent phenomena and proximity effects in two-dimensional magnets and heterostructures

Ultrathin van der Waals materials and their heterostructures offer a simple, yet powerful platform for discovering emergent phenomena and implementing device structures in the two-dimensional limit. The past few years has pushed this frontier to include magnetism. These advances have brought forth a new assortment of layered materials that intrinsically possess a wide variety of magnetic properties and are instrumental in integrating exchange and spin-orbit interactions into van der Waals heterostructures. This Review Article summarizes recent progress in exploring the intrinsic magnetism of atomically thin van der Waals materials, manipulation of their magnetism by tuning the interlayer coupling, and device structures for spin- and valleytronic applications.

Magnetized topological insulator multilayers

We discuss the magnetic and topological properties of bulk crystals and quasi-two-dimensional (quasi-2D) thin films formed by stacking intrinsic magnetized topological insulator (for example, Mn ([Formula: see text])2X4 with X = Se,Te) septuple layers and topological insulator quintuple layers in arbitrary order. Our analysis makes use of a simplified model that retains only Dirac cone degrees of freedom on both surfaces of each septuple or quintuple layer. We demonstrate the model's applicability and estimate its parameters by comparing with ab initio density-functional theory (DFT) calculations. We then employ the coupled Dirac cone model to provide an explanation for the dependence of thin-film properties, particularly the presence or absence of the quantum anomalous Hall effect, on film thickness, magnetic configuration, and stacking arrangement, and to comment on the design of Weyl superlattices.

Te-Vacancy-Induced Surface Collapse and Reconstruction in Antiferromagnetic Topological Insulator MnBi2Te4

MnBi₂Te₄ is an antiferromagnetic topological insulator that has stimulated intense interest due to its exotic quantum phenomena and promising device applications. The surface structure is a determinant factor to understand the magnetic and topological behavior of MnBi₂Te₄, yet its precise atomic structure remains elusive. Here we discovered a surface collapse and reconstruction of few-layer MnBi₂Te₄ exfoliated under delicate protection. Instead of the ideal septuple-layer structure in the bulk, the collapsed surface is shown to reconstruct as a Mn-doped Bi₂Te₃ quintuple layer and a Mn_xBi_yTe double layer with a clear van der Waals gap in between. Combined with first-principles calculations, such surface collapse is attributed to the abundant intrinsic Mn-Bi antisite defects and the tellurium vacancy in the exfoliated surface, which is further supported by in situ annealing and electron irradiation experiments. Our results shed light on the understanding of the intricate surface-bulk correspondence of MnBi₂Te₄ and provide an insightful perspective on the surface-related quantum measurements in MnBi₂Te₄ few-layer devices.

3D Quantum Hall Effect and a Global Picture of Edge States in Weyl Semimetals

We investigate the 3D quantum Hall effect in Weyl semimetals and elucidate a global picture of the edge states. The edge states hosting 3D quantum Hall effect are combinations of Fermi arcs and chiral Landau bands dispersing along the magnetic field direction. The Hall conductance, σ_{xz}^{H} [see Fig. 4], shows quantized plateaus with the variance of the magnetic field when the Fermi level is at the Weyl node. However, the chiral Landau bands can change the spatial distribution of the edge states, especially under a tilted magnetic field, and the resulting edge states lead to distinctive Hall transport phenomena. A tilted magnetic field contributes an intrinsic value to σ_{xz}^{H} and such an intrinsic value is determined by the tilting angle θ between the magnetic field and the y axis [see Fig. 1(c)]. Particularly, even if the perpendicular magnetic field is fixed, σ_{xz}^{H} will change its sign with an abrupt spatial shift of the edge states when θ exceeds a critical angle θ_{c}. Our work uncovers the novel edge-state nature of the 3D quantum Hall effect in Weyl semimetals.

Metamagnetism of Weakly Coupled Antiferromagnetic Topological Insulators

The magnetic properties of the van der Waals magnetic topological insulators MnBi_{2}Te_{4} and MnBi_{4}Te_{7} are investigated by magnetotransport measurements. We evidence that the relative strength of the interlayer exchange coupling J to the uniaxial anisotropy K controls a transition from an A-type antiferromagnetic order to a ferromagneticlike metamagnetic state. A bilayer Stoner-Wohlfarth model allows us to describe this evolution, as well as the typical angular dependence of specific signatures, such as the spin-flop transition of the uniaxial antiferromagnet and the switching field of the metamagnet.

Exchange bias and quantum anomalous nomalous Hall effect in the MnBi2Te4/CrI3 heterostructure

The layered antiferromagnetic MnBi2Te4 films have been proposed to be an intrinsic quantum anomalous Hall (QAH) insulator with a large gap. It is crucial to open a magnetic gap of surface states. However, recent experiments have observed gapless surface states, indicating the absence of out-of-plane surface magnetism, and thus, the quantized Hall resistance can only be achieved at the magnetic field above 6 T. We propose to induce out-of-plane surface magnetism of MnBi2Te4 films via the magnetic proximity with magnetic insulator CrI3. A strong exchange bias of ∼40 meV originates from the long Cr-eg orbital tails that hybridize strongly with Te p orbitals. By stabilizing surface magnetism, the QAH effect can be realized in the MnBi2Te4/CrI3 heterostructure. Moreover, the high-Chern number QAH state can be achieved by controlling external electric gates. Thus, the MnBi2Te4/CrI3 heterostructure provides a promising platform to realize the electrically tunable zero-field QAH effect.