Tunable quantum anomalous Hall effects in ferromagnetic van der Waals heterostructures

The quantum anomalous Hall effect (QAHE) has unique advantages in topotronic applications, but it is still challenging to realize the QAHE with tunable magnetic and topological properties for building functional devices. Through systematic first-principles calculations, we predict that the in-plane magnetization induced QAHE with Chern numbers C = ±1 and the out-of-plane magnetization induced QAHE with high Chern numbers C = ±3 can be realized in a single material candidate, which is composed of van der Waals (vdW) coupled Bi and MnBi2Te4 monolayers. The switching between different phases of QAHE can be controlled in multiple ways, such as applying strain or (weak) magnetic field or twisting the vdW materials. The prediction of an experimentally available material system hosting robust, highly tunable QAHE will stimulate great research interest in the field. Our work opens a new avenue for the realization of tunable QAHE and provides a practical material platform for the development of topological electronics.

Unveiling the Anomalous Hall Response of the Magnetic Structure Changes in the Epitaxial MnBi2Te4 Films

Recently discovered as an intrinsic antiferromagnetic topological insulator, MnBi2Te4 has attracted tremendous research interest, as it provides an ideal platform to explore the interplay between topological and magnetic orders. MnBi2Te4 displays distinct exotic topological phases that are inextricably linked to the different magnetic structures of the material. In this study, we conducted electrical transport measurements and systematically investigated the anomalous Hall response of epitaxial MnBi2Te4 films when subjected to an external magnetic field sweep, revealing the different magnetic structures stemming from the interplay of applied fields and the material's intrinsic antiferromagnetic (AFM) ordering. Our results demonstrate that the nonsquare anomalous Hall loop is a consequence of the distinct reversal processes within individual septuple layers. These findings shed light on the intricate magnetic structures in MnBi2Te4 and related materials, offering insights into understanding their transport properties and facilitating the implementation of AFM topological electronics.

Progress on the antiferromagnetic topological insulator MnBi2Te4

Topological materials, which feature robust surface and/or edge states, have now been a research focus in condensed matter physics. They represent a new class of materials exhibiting nontrivial topological phases, and provide a platform for exploring exotic transport phenomena, such as the quantum anomalous Hall effect and the quantum spin Hall effect. Recently, magnetic topological materials have attracted considerable interests due to the possibility to study the interplay between topological and magnetic orders. In particular, the quantum anomalous Hall and axion insulator phases can be realized in topological insulators with magnetic order. MnBi2Te4, as the first intrinsic antiferromagnetic topological insulator discovered, allows the examination of existing theoretical predictions; it has been extensively studied, and many new discoveries have been made. Here we review the progress made on MnBi2Te4 from both experimental and theoretical aspects. The bulk crystal and magnetic structures are surveyed first, followed by a review of theoretical calculations and experimental probes on the band structure and surface states, and a discussion of various exotic phases that can be realized in MnBi2Te4. The properties of MnBi2Te4 thin films and the corresponding transport studies are then reviewed, with an emphasis on the edge state transport. Possible future research directions in this field are also discussed.

On the topological surface states of the intrinsic magnetic topological insulator Mn-Bi-Te family

We review recent progress in the electronic structure study of intrinsic magnetic topological insulators (MnBi2Te4) · (Bi2Te3)n ([Formula: see text]) family. Specifically, we focus on the ubiquitously (nearly) gapless behavior of the topological Dirac surface state observed by photoemission spectroscopy, even though a large Dirac gap is expected because of surface ferromagnetic order. The dichotomy between experiment and theory concerning this gap behavior is perhaps the most critical and puzzling question in this frontier. We discuss various proposals accounting for the lack of magnetic effect on the topological Dirac surface state, which are mainly categorized into two pictures, magnetic reconfiguration and topological surface state redistribution. Band engineering towards opening a magnetic gap of topological surface states provides great opportunities to realize quantized topological transport and axion electrodynamics at higher temperatures.

Recent progress in MnBi2nTe3n+1 intrinsic magnetic topological insulators: crystal growth, magnetism and chemical disorder

The search for magnetic topological materials has been at the forefront of condensed matter research for their potential to host exotic states such as axion insulators, magnetic Weyl semimetals, Chern insulators, etc. To date, the MnBi2nTe3n+1 family is the only group of materials showcasing van der Waals-layered structures, intrinsic magnetism and non-trivial band topology without trivial bands at the Fermi level. The interplay between magnetism and band topology in this family has led to the proposal of various topological phenomena, including the quantum anomalous Hall effect, quantum spin Hall effect and quantum magnetoelectric effect. Among these, the quantum anomalous Hall effect has been experimentally observed at record-high temperatures, highlighting the unprecedented potential of this family of materials in fundamental science and technological innovation. In this paper, we provide a comprehensive review of the research progress in this intrinsic magnetic topological insulator family, with a focus on single-crystal growth, characterization of chemical disorder, manipulation of magnetism through chemical substitution and external pressure, and important questions that remain to be conclusively answered.

Pressure-cycling induced transition behaviors of MnBi2Te4

MnBi2Te4 can generate a variety of exotic topological quantum states, which are closely related to its special structure. We conduct comprehensive multiple-cycle high-pressure research on MnBi2Te4 by using a diamond anvil cell to study its phase transition behaviors under high pressure. As observed, when the pressure does not exceed 15 GPa, the material undergoes an irreversible metal-semiconductor-metal transition, whereas when the pressure exceeds 17 GPa, the layered structure is damaged and becomes irreversibly amorphous due to the lattice distortion caused by compression, but it is not completely amorphous, which presents some nano-sized grains after decompression. Our investigation vividly reveals the phase transition behaviors of MnBi2Te4 under high pressure cycling and paves the experimental way to find topological phases under high pressure.

Phase Separation Prevents the Synthesis of VBi2Te4 by Molecular Beam Epitaxy

Intrinsic magnetic topological insulators (IMTIs) have a non-trivial band topology in combination with magnetic order. This potentially leads to fascinating states of matter, such as quantum anomalous Hall (QAH) insulators and axion insulators. One of the theoretically predicted IMTIs is VBi2Te4, but experimental evidence of this material is lacking so far. Here, we report on our attempts to synthesise VBi2Te4 by molecular beam epitaxy (MBE). X-ray diffraction reveals that in the thermodynamic phase space reachable by MBE, there is no region where VBi2Te4 is stably synthesised. Moreover, scanning transmission electron microscopy shows a clear phase separation to Bi2Te3 and VTe2 instead of the formation of VBi2Te4. We suggest the phase instability to be due to either the large lattice mismatch between VTe2 and Bi2Te3 or the unfavourable valence state of vanadium.

Crossover from gapped-to-gapless Dirac surface states in magnetic topological insulator MnBi2Te4

Intrinsic magnetic topological insulators (MTIs) host exotic topological phases such as quantized anomalous Hall insulating phase, arising due to the large magnetic exchange gap. However, the interplay of magnetism and topology in these systems in different temperature regimes remains elusive. In this work, we present the logarithmic temperature-dependence of conductivity for sub-100 nm thick exfoliated flakes of MTI MnBi2Te4in the presence of out-of-plane magnetic fields and extracted the linear slope,κ. We observed a characteristic change,Δκ∼-0.5in the low-temperature regime, indicating the gapped Dirac surface state according to Lu-Shen theory. We also report the recovery of topological properties in the system via the weak-antilocalization effect in the vicinity of antiferromagnetic to paramagnetic transition and in the paramagnetic regime. Hikami-Larkin-Nagaoka analysis suggested the presence of topological surface states. Therefore, our study helps in understanding how intrinsic magnetism masks topological properties in an MTI as long as magnetic ordering persists.

Magnetic Topological Insulator MnBi2Te4 Nanosheets for Femtosecond Pulse Generation

The van der Waals layered material MnBi2Te4, as a magnetic topological insulator, has attracted tremendous interest for novel physics research in the fields of condensed matter physics and materials science. However, the nonlinear optical properties of MnBi2Te4 and its applications in ultrafast optics have rarely been explored. In this study, high-quality MnBi2Te4 nanosheets have been successfully synthesized by the self-flux method. The morphology, chemical composition, magnetic properties, and nonlinear optical characteristics were systematically investigated. The magnetic transition of MnBi2Te4 was confirmed by a low-temperature spatially resolved spectroscopic technique. The saturable absorption property of MnBi2Te4 was measured by a balanced twin-detector system with a modulation depth of 4.5% and a saturation optical intensity of 2.35 GW/cm2. Furthermore, by inserting the MnBi2Te4-based saturable absorber, a soliton mode-locking laser operating at 1558.8 nm was obtained with a pulse duration of 331 fs. This research will pave the way for applications of the magnetic TI MnBi2Te4 in nonlinear optics and photonics.

Exploring the Epitaxial Growth Kinetics and Anomalous Hall Effect in Magnetic Topological Insulator MnBi2Te4 Films

The discovery of MnBi2Te4-based intrinsic magnetic topological insulators has fueled tremendous interest in condensed matter physics, owing to their potential as an ideal platform for exploring the quantum anomalous Hall effect and other magnetism-topology interactions. However, the fabrication of single-phase MnBi2Te4 films remains a common challenge in the research field. Herein, we present an effective and simple approach for fabricating high-quality, near-stoichiometric MnBi2Te4 films by directly matching the growth rates of intermediate Bi2Te3 and MnTe. Through systematic experimental studies and thermodynamic calculations, we demonstrate that binary phases of Bi2Te3 and MnTe are easily formed during film growth, and the reaction of Bi2Te3 + MnTe → MnBi2Te4 represents the rate-limiting step among all possible reaction paths, which could result in the presence of Bi2Te3 and MnTe impurity phases in the grown MnBi2Te4 films. Moreover, Bi2Te3 and MnTe impurities introduce negative and positive anomalous Hall (AH) components, respectively, in the AH signals of MnBi2Te4 films. Our work suggests that further manipulation of growth parameters should be the essential route for fabricating phase-pure MnBi2Te4 films.

Mesoporous Semiconductive Bi2Se3 Films

Bi₂Se₃ is a semiconductive material possessing a bandgap of 0.3 eV, and its unique band structure has paved the way for diverse applications. Herein, we demonstrate a robust platform for synthesizing mesoporous Bi₂Se₃ films with uniform pore sizes via electrodeposition. Block copolymer micelles act as soft templates in the electrolyte to create a 3D porous nanoarchitecture. By controlling the length of the block copolymer, the pore size is adjusted to 9 and 17 nm precisely. The nonporous Bi₂Se₃ film exhibits a tunneling current in a vertical direction of 52.0 nA, but upon introducing porosity (9 nm pores), the tunneling current increases significantly to 684.6 nA, suggesting that the conductivity of Bi₂Se₃ films is dependent on the pore structure and surface area. The abundant porous architecture exposes a larger surface area of Bi₂Se₃ to the surrounding air within the same volume, thereby augmenting its metallic properties.

High Curie temperature ferromagnetic structures of (Sb2Te3)1-x(MnSb2Te4)x with x = 0.7-0.8

Magnetic topological materials are promising for realizing novel quantum physical phenomena. Among these, bulk Mn-rich MnSb₂Te₄ is ferromagnetic due to Mn_Sb antisites and has relatively high Curie temperatures (T_C), which is attractive for technological applications. We have previously reported the growth of materials with the formula (Sb₂Te₃)_1-x(MnSb₂Te₄)_x, where x varies between 0 and 1. Here we report on their magnetic and transport properties. We show that the samples are divided into three groups based on the value of x (or the percent septuple layers within the crystals) and their corresponding T_C values. Samples that contain x < 0.7 or x > 0.9 have a single T_C value of 15-20 K and 20-30 K, respectively, while samples with 0.7 < x < 0.8 exhibit two T_C values, one (T_C1) at ~ 25 K and the second (T_C2) reaching values above 80 K, almost twice as high as any reported value to date for these types of materials. Structural analysis shows that samples with 0.7 < x < 0.8 have large regions of only SLs, while other regions have isolated QLs embedded within the SL lattice. We propose that the SL regions give rise to a T_C1 of ~ 20 to 30 K, and regions with isolated QLs are responsible for the higher T_C2 values. Our results have important implications for the design of magnetic topological materials having enhanced properties.

Visualizing the interplay of Dirac mass gap and magnetism at nanoscale in intrinsic magnetic topological insulators

In intrinsic magnetic topological insulators, Dirac surface-state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here, we use molecular beam epitaxy to grow intrinsic MnBi₂Te₄ thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that, in high defect regions, the Dirac mass gap collapses. Ab initio and coupled Dirac cone model calculations provide insight into the microscopic origin of the correlation between defect density and spatial gap variations. This work provides unambiguous identification of the Dirac mass gap in MnBi₂Te₄ and, by revealing the microscopic origin of its gap variation, establishes a material design principle for realizing exotic states in intrinsic magnetic topological insulators.

Evolution of the Electronic Structure of Ultrathin MnBi2Te4 Films

Ultrathin films of intrinsic magnetic topological insulator MnBi₂Te₄ exhibit fascinating quantum properties such as the quantum anomalous Hall effect and the axion insulator state. In this work, we systematically investigate the evolution of the electronic structure of MnBi₂Te₄ thin films. With increasing film thickness, the electronic structure changes from an insulator type with a large energy gap to one with in-gap topological surface states, which is, however, still in drastic contrast to the bulk material. By surface doping of alkali-metal atoms, a Rashba split band gradually emerges and hybridizes with topological surface states, which not only reconciles the puzzling difference between the electronic structures of the bulk and thin-film MnBi₂Te₄ but also provides an interesting platform to establish Rashba ferromagnet that is attractive for (quantum) anomalous Hall effect. Our results provide important insights into the understanding and engineering of the intriguing quantum properties of MnBi₂Te₄ thin films.

Unconventional Pressure-Driven Metamagnetic Transitions in Topological van der Waals Magnets

Activating metamagnetic transitions between ordered states in van der Waals magnets and devices bring great opportunities in spintronics. We show that external pressure, which enhances the interlayer hopping without introducing chemical disorders, triggers multiple metamagnetic transitions upon cooling in the topological van der Waals magnets Mn(Bi_1-xSb_x)₄Te₇, where the antiferromagnetic interlayer superexchange coupling competes with the ferromagnetic interlayer coupling mediated by the antisite Mn spins. The temperature-pressure phase diagrams reveal that while the ordering temperature from the paramagnetic to ordered states is almost pressure-independent, the metamagnetic transitions show nontrivial pressure and temperature dependence, even re-entrance. For these highly anisotropic magnets, we attribute the former to the ordering temperature being only weakly dependent on the intralayer parameters and the latter to the parametrically different pressure and temperature dependence of the two interlayer couplings. Our independent probing of these disparate magnetic interactions paves an avenue for efficient magnetic manipulations in van der Waals magnets.

Approaching a Minimal Topological Electronic Structure in Antiferromagnetic Topological Insulator MnBi2Te4 via Surface Modification

The topological electronic structure plays a central role in the nontrivial physical properties in topological quantum materials. A minimal, "hydrogen-atom-like" topological electronic structure is desired for research. In this work, we demonstrate an effort toward the realization of such a system in the intrinsic magnetic topological insulator MnBi₂Te₄, by manipulating the topological surface state (TSS) via surface modification. Using high resolution laser- and synchrotron-based angle-resolved photoemission spectroscopy (ARPES), we found the TSS in MnBi₂Te₄ is heavily hybridized with a trivial Rashba-type surface state (RSS), which could be efficiently removed by the in situ surface potassium (K) dosing. By employing multiple experimental methods to characterize K dosed surface, we attribute such a modification to the electrochemical reactions of K clusters on the surface. Our work not only gives a clear band assignment in MnBi₂Te₄ but also provides possible new routes in accentuating the topological behavior in the magnetic topological quantum materials.

Observation of Ultrastrong Coupling between Substrate and the Magnetic Topological Insulator MnBi2Te4

The intrinsic magnetic topological insulator MnBi₂Te₄ has attracted significant interest recently as a promising platform for exploring exotic quantum phenomena. Here we report that, when atomically thin MnBi₂Te₄ is deposited on a substrate such as silicon oxide or gold, there is a very strong mechanical coupling between the atomic layer and the supporting substrate. This is manifested as an intense low-frequency breathing Raman mode that is present even for monolayer MnBi₂Te₄. Interestingly, this coupling turns out to be stronger than the interlayer coupling between the MnBi₂Te₄ atomic layers. We further found that these low-energy breathing modes are highly sensitive to sample degradation, and they become drastically weaker upon ambient air exposure. This is in contrast to the higher energy optical phonon modes which are much more robust, suggesting that the low-energy Raman modes found here can be an effective indicator of sample quality.

Magnetic Topological Insulator Heterostructures: A Review

Topological insulators (TIs) provide intriguing prospects for the future of spintronics due to their large spin-orbit coupling and dissipationless, counter-propagating conduction channels in the surface state. The combination of topological properties and magnetic order can lead to new quantum states including the quantum anomalous Hall effect that was first experimentally realized in Cr-doped (Bi,Sb)₂ Te₃ films. Since magnetic doping can introduce detrimental effects, requiring very low operational temperatures, alternative approaches are explored. Proximity coupling to magnetically ordered systems is an obvious option, with the prospect to raise the temperature for observing the various quantum effects. Here, an overview of proximity coupling and interfacial effects in TI heterostructures is presented, which provides a versatile materials platform for tuning the magnetic and topological properties of these exciting materials. An introduction is first given to the heterostructure growth by molecular beam epitaxy and suitable structural, electronic, and magnetic characterization techniques. Going beyond transition-metal-doped and undoped TI heterostructures, examples of heterostructures are discussed, including rare-earth-doped TIs, magnetic insulators, and antiferromagnets, which lead to exotic phenomena such as skyrmions and exchange bias. Finally, an outlook on novel heterostructures such as intrinsic magnetic TIs and systems including 2D materials is given.

Mn-Rich MnSb2 Te4 : A Topological Insulator with Magnetic Gap Closing at High Curie Temperatures of 45-50 K

Ferromagnetic topological insulators exhibit the quantum anomalous Hall effect, which is potentially useful for high-precision metrology, edge channel spintronics, and topological qubits.  The stable 2+ state of Mn enables intrinsic magnetic topological insulators. MnBi2 Te4 is, however, antiferromagnetic with 25 K Néel temperature and is strongly n-doped. In this work, p-type MnSb2 Te4 , previously considered topologically trivial, is shown to be a ferromagnetic topological insulator for a few percent Mn excess. i) Ferromagnetic hysteresis with record Curie temperature of 45-50 K, ii) out-of-plane magnetic anisotropy, iii) a 2D Dirac cone with the Dirac point close to the Fermi level, iv) out-of-plane spin polarization as revealed by photoelectron spectroscopy, and v) a magnetically induced bandgap closing at the Curie temperature, demonstrated by scanning tunneling spectroscopy (STS), are shown. Moreover, a critical exponent of the magnetization β ≈ 1 is found, indicating the vicinity of a quantum critical point. Ab initio calculations reveal that Mn-Sb site exchange provides the ferromagnetic interlayer coupling and the slight excess of Mn nearly doubles the Curie temperature. Remaining deviations from the ferromagnetic order open the inverted bulk bandgap and render MnSb2 Te4 a robust topological insulator and new benchmark for magnetic topological insulators.

Thermoelectric degrees of freedom determining thermoelectric efficiency

For over half a century, the development of thermoelectric materials has based on the dimensionless figure of merit zT, assuming that the efficiency is mainly determined by this single parameter. Here, we show that the thermoelectric conversion efficiency is determined by three independent parameters, Zgen, τ, and β, which we call the three thermoelectric degrees of freedom (DoFs). Zgen is the well-defined mean of the traditional zT under nonzero temperature differences. The two additional parameters τ and β are gradients of material properties and crucial to evaluating the heat current altered by nonzero Thomson heat and asymmetric Joule heat escape. Each parameter is a figure of merit. Therefore, increasing one of the three DoFs leads to higher efficiency. Our finding explains why the single-parameter theory is inaccurate. Further, it suggests an alternative direction in material discovery and device design in thermoelectrics, such as high τ and β, beyond zT.

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General efficiency theory of thermoelectric conversion is derived for T-dependent properties

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Three degrees of freedom Z_gen, τ, and β determine thermoelectric efficiency

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Efficiency can vary up to approximately 40% with τ and β

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Each degree of freedom is a figure of merit

Crossover from 2D Ferromagnetic Insulator to Wide Band Gap Quantum Anomalous Hall Insulator in Ultrathin MnBi2Te4

Intrinsic magnetic topological insulators offer low disorder and large magnetic band gaps for robust magnetic topological phases operating at higher temperatures. By controlling the layer thickness, emergent phenomena such as the quantum anomalous Hall (QAH) effect and axion insulator phases have been realized. These observations occur at temperatures significantly lower than the Néel temperature of bulk MnBi₂Te₄, and measurement of the magnetic energy gap at the Dirac point in ultrathin MnBi₂Te₄ has yet to be achieved. Critical to achieving the promise of this system is a direct measurement of the layer-dependent energy gap and verification of a temperature-dependent topological phase transition from a large band gap QAH insulator to a gapless TI paramagnetic phase. Here we utilize temperature-dependent angle-resolved photoemission spectroscopy to study epitaxial ultrathin MnBi₂Te₄. We directly observe a layer-dependent crossover from a 2D ferromagnetic insulator with a band gap greater than 780 meV in one septuple layer (1 SL) to a QAH insulator with a large energy gap (>70 meV) at 8 K in 3 and 5 SL MnBi₂Te₄. The QAH gap is confirmed to be magnetic in origin, as it becomes gapless with increasing temperature above 8 K.

Recent Progress in Proximity Coupling of Magnetism to Topological Insulators

Inducing long-range magnetic order in 3D topological insulators can gap the Dirac-like metallic surface states, leading to exotic new phases such as the quantum anomalous Hall effect or the axion insulator state. These magnetic topological phases can host robust, dissipationless charge and spin currents or unique magnetoelectric behavior, which can be exploited in low-energy electronics and spintronics applications. Although several different strategies have been successfully implemented to realize these states, to date these phenomena have been confined to temperatures below a few Kelvin. This review focuses on one strategy: inducing magnetic order in topological insulators by proximity of magnetic materials, which has the capability for room temperature operation, unlocking the potential of magnetic topological phases for applications. The unique advantages of this strategy, the important physical mechanisms facilitating magnetic proximity effect, and the recent progress to achieve, understand, and harness proximity-coupled magnetic order in topological insulators are discussed. Some emerging new phenomena and applications enabled by proximity coupling of magnetism and topological materials, such as skyrmions and the topological Hall effect, are also highlighted, and the authors conclude with an outlook on remaining challenges and opportunities in the field.

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.

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van der Waals material MnBi₂Te₄ is an intrinsic antiferromagnetic topological insulator

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Under moderate magnetic field, MnBi₂Te₄ may become a magnetic Weyl semimetal

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MnBi₂Te₄ and its family of materials have brought great progress in studying novel topological quantum states

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Quantum anomalous Hall effect above the liquid-nitrogen temperature can be expected in MnBi₂Te₄-related systems

Intercalated architecture of MA2Z4 family layered van der Waals materials with emerging topological, magnetic and superconducting properties

The search for new two-dimensional monolayers with diverse electronic properties has attracted growing interest in recent years. Here, we present an approach to construct MA2Z4 monolayers with a septuple-atomic-layer structure, that is, intercalating a MoS2-type monolayer MZ2 into an InSe-type monolayer A2Z2. We illustrate this unique strategy by means of first-principles calculations, which not only reproduce the structures of MoSi2N4 and MnBi2Te4 that were already experimentally synthesized, but also predict 72 compounds that are thermodynamically and dynamically stable. Such an intercalated architecture significantly reconstructs the band structures of the constituents MZ2 and A2Z2, leading to diverse electronic properties for MA2Z4, which can be classified according to the total number of valence electrons. The systems with 32 and 34 valence electrons are mostly semiconductors. Whereas, those with 33 valence electrons can be nonmagnetic metals or ferromagnetic semiconductors. In particular, we find that, among the predicted compounds, (Ca,Sr)Ga2Te4 are topologically nontrivial by both the standard density functional theory and hybrid functional calculations. While VSi2P4 is a ferromagnetic semiconductor and TaSi2N4 is a type-I Ising superconductor. Moreover, WSi2P4 is a direct gap semiconductor with peculiar spin-valley properties, which are robust against interlayer interactions. Our study thus provides an effective way of designing septuple-atomic-layer MA2Z4 with unusual electronic properties to draw immediate experimental interest.

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.

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.

Realization of an intrinsic ferromagnetic topological state in MnBi8Te13

Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.

Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator

The intricate interplay between non-trivial topology and magnetism in two-dimensional materials can lead to the emergence of interesting phenomena such as the quantum anomalous Hall effect. Here we investigate the quantum transport of both bulk crystal and exfoliated MnBi₂Te₄ flakes in a field-effect transistor geometry. For the six septuple-layer device tuned into the insulating regime, we observe a large longitudinal resistance and zero Hall plateau, which are characteristics of an axion insulator state. The robust axion insulator state occurs in zero magnetic field, over a wide magnetic-field range and at relatively high temperatures. Moreover, a moderate magnetic field drives a quantum phase transition from the axion insulator phase to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance h/e², where h is Planck's constant and e is electron charge. Our results pave the way for using even-number septuple-layer MnBi₂Te₄ to realize the quantized topological magnetoelectric effect and axion electrodynamics in condensed matter systems.

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

The quantum Hall effect (QHE) with quantized Hall resistance of h/νe² started the research on topological quantum states and laid the foundation of topology in physics. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). Here, we report the experimental discovery of high-Chern-number QHE (C = 2) without Landau levels and C = 1 Chern insulator state displaying a nearly quantized Hall resistance plateau above the Néel temperature in MnBi₂Te₄ devices. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures.

Crystal Chemistry and Bonding Patterns of Bismuth-Based Topological Insulators

Bismuth is gaining importance as a key element of functional quantum materials. The effects of spin-orbit coupling (SOC) are at the heart of many exciting proposals for next-generation quantum technologies, including topological materials for efficient information transmission and energy-saving applications. The "heavy" element bismuth and its compounds are predestined for SOC-induced topological properties, but materials design is challenged by a complex link between them and the chemical composition and crystal structure. Nevertheless, a lot can be learned about a certain property by testing its limits with compositional and/or structure modifications. We survey a handful of topological bismuth-based materials that bear structural and chemical semblance to the early topological insulators, antimony-doped elemental bismuth, Bi₂Se₃ and Bi₂Te₃. Chemical bonding via p orbitals and modular structure underlie all considered bismuth chalcogenides, subhalides, and chalcogenide halides and allow us to correlate the evolution of chemical bonding and structure with variability of the topological properties, although materials design should not be regarded as a building blocks set. Over the past decade, material discoveries have unearthed a plethora of topological properties, and bismuth is very fertile as a progenitor of a rich palette of exotic quantum materials, ranging from strong and weak 3D and crystalline topological insulators over topological metals and semimetals to magnetic topological insulators, while preserving the general layered structure motif.

A van der Waals antiferromagnetic topological insulator with weak interlayer magnetic coupling

Magnetic topological insulators (TI) provide an important material platform to explore quantum phenomena such as quantized anomalous Hall effect and Majorana modes, etc. Their successful material realization is thus essential for our fundamental understanding and potential technical revolutions. By realizing a bulk van der Waals material MnBi4Te7 with alternating septuple [MnBi2Te4] and quintuple [Bi2Te3] layers, we show that it is ferromagnetic in plane but antiferromagnetic along the c axis with an out-of-plane saturation field of ~0.22 T at 2 K. Our angle-resolved photoemission spectroscopy measurements and first-principles calculations further demonstrate that MnBi4Te7 is a Z2 antiferromagnetic TI with two types of surface states associated with the [MnBi2Te4] or [Bi2Te3] termination, respectively. Additionally, its superlattice nature may make various heterostructures of [MnBi2Te4] and [Bi2Te3] layers possible by exfoliation. Therefore, the low saturation field and the superlattice nature of MnBi4Te7 make it an ideal system to investigate rich emergent phenomena.

Antiferromagnetic topological insulator MnBi2Te4: synthesis and magnetic properties

Recently, MnBi2Te4 has been discovered as the first intrinsic antiferromagnetic topological insulator (AFM TI), and it will become a promising material to discover exotic topological quantum phenomena. In this work, we have realized the successful synthesis of high-quality MnBi2Te4 single crystals by solid-state reactions. The as-grown MnBi2Te4 single crystal exhibits a van der Waals layered structure, which is composed of septuple Te-Bi-Te-Mn-Te-Bi-Te sequences as determined by X-ray diffraction and high-resolution high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM). The magnetic order below 25 K as a consequence of A-type antiferromagnetic interaction between Mn layers in the MnBi2Te4 crystal suggests the unique interplay between antiferromagnetism and topological quantum states. Moreover, the transport measurements of MnBi2Te4 single crystals further confirm its magnetic transition. This study on the first AFM TI of MnBi2Te4 will guide the future research on other potential candidates in the MBixTey family (M = Ni, V, Ti, etc.).

Prediction and observation of an antiferromagnetic topological insulator

Magnetic topological insulators are narrow-gap semiconductor materials that combine non-trivial band topology and magnetic order¹. Unlike their nonmagnetic counterparts, magnetic topological insulators may have some of the surfaces gapped, which enables a number of exotic phenomena that have potential applications in spintronics¹, such as the quantum anomalous Hall effect² and chiral Majorana fermions³. So far, magnetic topological insulators have only been created by means of doping nonmagnetic topological insulators with 3d transition-metal elements; however, such an approach leads to strongly inhomogeneous magnetic⁴ and electronic⁵ properties of these materials, restricting the observation of important effects to very low temperatures^2,3. An intrinsic magnetic topological insulator-a stoichiometric well ordered magnetic compound-could be an ideal solution to these problems, but no such material has been observed so far. Here we predict by ab initio calculations and further confirm using various experimental techniques the realization of an antiferromagnetic topological insulator in the layered van der Waals compound MnBi₂Te₄. The antiferromagnetic ordering  that MnBi₂Te₄  shows makes it invariant with respect to the combination of the time-reversal and primitive-lattice translation symmetries, giving rise to a ℤ₂ topological classification; ℤ₂ = 1 for MnBi₂Te₄, confirming its topologically nontrivial nature. Our experiments indicate that the symmetry-breaking (0001) surface of MnBi₂Te₄ exhibits a large bandgap in the topological surface state. We expect this property to eventually enable the observation of a number of fundamental phenomena, among them quantized magnetoelectric coupling^6-8 and axion electrodynamics^9,10. Other exotic phenomena could become accessible at much higher temperatures than those reached so far, such as the quantum anomalous Hall effect² and chiral Majorana fermions³.

Intrinsic magnetic topological insulator phases in the Sb doped MnBi2Te4 bulks and thin flakes

Magnetic topological insulators (MTIs) offer a combination of topologically nontrivial characteristics and magnetic order and show promise in terms of potentially interesting physical phenomena such as the quantum anomalous Hall (QAH) effect and topological axion insulating states. However, the understanding of their properties and potential applications have been limited due to a lack of suitable candidates for MTIs. Here, we grow two-dimensional single crystals of Mn(SbxBi(1-x))2Te4 bulk and exfoliate them into thin flakes in order to search for intrinsic MTIs. We perform angle-resolved photoemission spectroscopy, low-temperature transport measurements, and first-principles calculations to investigate the band structure, transport properties, and magnetism of this family of materials, as well as the evolution of their topological properties. We find that there exists an optimized MTI zone in the Mn(SbxBi(1-x))2Te4 phase diagram, which could possibly host a high-temperature QAH phase, offering a promising avenue for new device applications.

Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials

The interplay of magnetism and topology is a key research subject in condensed matter physics, which offers great opportunities to explore emerging new physics, such as the quantum anomalous Hall (QAH) effect, axion electrodynamics, and Majorana fermions. However, these exotic physical effects have rarely been realized experimentally because of the lack of suitable working materials. Here, we predict a series of van der Waals layered MnBi2Te4-related materials that show intralayer ferromagnetic and interlayer antiferromagnetic exchange interactions. We find extremely rich topological quantum states with outstanding characteristics in MnBi2Te4, including an antiferromagnetic topological insulator with the long-sought topological axion states on the surface, a type II magnetic Weyl semimetal with one pair of Weyl points, as well as a collection of intrinsic axion insulators and QAH insulators in even- and odd-layer films, respectively. These notable predictions, if proven experimentally, could profoundly change future research and technology of topological quantum physics.

Topological Axion States in the Magnetic Insulator MnBi_{2}Te_{4} with the Quantized Magnetoelectric Effect

Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant topological states in quantum materials has made tremendous progress. However, the study of magnetic topological states falls much behind due to the complex magnetic structures. Here, we predict the tetradymite-type compound MnBi_{2}Te_{4} and its related materials host topologically nontrivial magnetic states. The magnetic ground state of MnBi_{2}Te_{4} is an antiferromagetic topological insulator state with a large topologically nontrivial energy gap (∼0.2  eV). It presents the axion state, which has gapped bulk and surface states, and the quantized topological magnetoelectric effect. The ferromagnetic phase of MnBi_{2}Te_{4} might lead to a minimal ideal Weyl semimetal.

Unique Thickness-Dependent Properties of the van der Waals Interlayer Antiferromagnet MnBi_{2}Te_{4} Films

Using density functional theory and Monte Carlo calculations, we study the thickness dependence of the magnetic and electronic properties of a van der Waals interlayer antiferromagnet in the two-dimensional limit. Considering MnBi_{2}Te_{4} as a model material, we find it to demonstrate a remarkable set of thickness-dependent magnetic and topological transitions. While a single septuple layer block of MnBi_{2}Te_{4} is a topologically trivial ferromagnet, the thicker films made of an odd (even) number of blocks are uncompensated (compensated) interlayer antiferromagnets, which show wide band gap quantum anomalous Hall (zero plateau quantum anomalous Hall) states. Thus, MnBi_{2}Te_{4} is the first stoichiometric material predicted to realize the zero plateau quantum anomalous Hall state intrinsically. This state has been theoretically shown to host the exotic axion insulator phase.

Realization of interlayer ferromagnetic interaction in MnSb2Te4 toward the magnetic Weyl semimetal state

Magnetic properties of MnSb2Te4 were examined through magnetic susceptibility, specific-heat, and neutron-diffraction measurements. As opposed to isostructural MnBi2Te4 with the antiferromagnetic ground state, MnSb2Te4 develops a spontaneous magnetization below 25 K. From our first-principles calculations on the material in a ferromagnetic state, the state could be interpreted as a type-II Weyl semimetal state with broken time-reversal symmetry. Detailed structural refinements using x-ray-diffraction and neutron-diffraction data reveal the presence of site mixing between Mn and Sb sites, leading to the ferrimagnetic ground state. With theoretical calculations, we found that the presence of site mixing plays an important role for the interlayer Mn-Mn ferromagnetic interactions.

New Universal Type of Interface in the Magnetic Insulator/Topological Insulator Heterostructures

Magnetic proximity effect at the interface between magnetic and topological insulators (MIs and TIs) is considered to have great potential in spintronics as, in principle, it allows realizing the quantum anomalous Hall and topological magneto-electric effects (QAHE and TME). Although an out-of-plane magnetization induced in a TI by the proximity effect was successfully probed in experiments, first-principles calculations reveal that a strong electrostatic potential mismatch at abrupt MI/TI interfaces creates harmful trivial states rendering both the QAHE and TME unfeasible in practice. Here on the basis of recent progress in formation of planar self-assembled single layer MI/TI heterostructure (T. Hirahara et al. Nano Lett. 2017 , 17 , 3493 - 3500 ), we propose a conceptually new type of the MI/TI interfaces by means of density functional theory calculations. By considering MnSe/Bi₂Se₃, MnTe/Bi₂Te₃, and EuS/Bi₂Se₃ we demonstrate that, instead of a sharp MI/TI interface clearly separating the two subsystems, it is energetically far more favorable to form a built-in interface via insertion of the MI film inside the TI's surface quintuple layer (e.g., Se-Bi-Se-[MnSe]-Bi-Se) where it forms a bulk-like MI structure. This results in a smooth MI-to-TI connection that yields the interface electronic structure essentially free of trivial states. Our findings open a new direction in studies of the MI/TI interfaces and restore their potential for the QAHE and TME observation.