High-precision realization of robust quantum anomalous Hall state in a hard ferromagnetic topological insulator

Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents

The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of e^{2}/h. Here we show that the quantum Hall effect is accompanied by an orbital Hall effect. Our quantum mechanical calculations fit well the semiclassical interpretation in terms of "skipping orbits." The chiral edge states of a quantum Hall system are orbital polarized akin to a hypothetical orbital version of the quantum anomalous Hall effect in magnetic systems. The orbital Hall resistivity scales quadratically with the magnetic field, making it the dominant effect at high fields.

Recent progress of MnBi2Te4 epitaxial thin films as a platform for realising the quantum anomalous Hall effect

Since the first realisation of the quantum anomalous Hall effect (QAHE) in a dilute magnetic-doped topological insulator thin film in 2013, the quantisation temperature has been limited to less than 1 K due to magnetic disorder in dilute magnetic systems. With magnetic moments ordered into the crystal lattice, the intrinsic magnetic topological insulator MnBi2Te4 has the potential to eliminate or significantly reduce magnetic disorder and improve the quantisation temperature. Surprisingly, to date, the QAHE has yet to be observed in molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films at zero magnetic field, and what leads to the difficulty in quantisation is still an active research area. Although bulk MnBi2Te4 and exfoliated flakes have been well studied, revealing both the QAHE and axion insulator phases, experimental progress on MBE thin films has been slower. Understanding how the breakdown of the QAHE occurs in MnBi2Te4 thin films and finding solutions that will enable mass-produced millimetre-size QAHE devices operating at elevated temperatures are required. In this mini-review, we will summarise recent studies on the electronic and magnetic properties of MBE MnBi2Te4 thin films and discuss mechanisms that could explain the failure of the QAHE from the aspects of defects, electronic structure, magnetic order, and consequences of their delicate interplay. Finally, we propose several strategies for realising the QAHE at elevated temperatures in MnBi2Te4 thin films.

Spin Gapless Quantum Materials and Devices

Quantum materials, with nontrivial quantum phenomena and mechanisms, promise efficient quantum technologies with enhanced functionalities. Quantum technology is held back because a gap between fundamental science and its implementation is not fully understood yet. In order to capitalize the quantum advantage, a new perspective is required to figure out and close this gap. In this review, spin gapless quantum materials, featured by fully spin-polarized bands and the electron/hole transport, are discussed from the perspective of fundamental understanding and device applications. Spin gapless quantum materials can be simulated by minimal two-band models and could help to understand band structure engineering in various topological quantum materials discovered so far. It is explicitly highlighted that various types of spin gapless band dispersion are fundamental ingredients to understand quantum anomalous Hall effect. Based on conventional transport in the bulk and topological transport on the boundaries, various spintronic device aspects of spin gapless quantum materials as well as their advantages in different models for topological field effect transistors are reviewed.

Atomic scale quantum anomalous hall effect in monolayer graphene/MnBi2Te4 heterostructure

The two-dimensional quantum anomalous Hall (QAH) effect is direct evidence of non-trivial Berry curvature topology in condensed matter physics. Searching for QAH in 2D materials, particularly with simplified fabrication methods, poses a significant challenge in future applications. Despite numerous theoretical works proposed for the QAH effect with C = 2 in graphene, neglecting magnetism sources such as proper substrate effects lacks experimental evidence. In this work, we propose the QAH effect in graphene/MnBi2Te4 (MBT) heterostructure based on density-functional theory (DFT) calculations. The monolayer MBT introduces spin-orbital coupling, Zeeman exchange field, and Kekulé distortion as a substrate effect into graphene, resulting in QAH with C = 1 in the heterostructure. Our effective Hamiltonian further presents a rich phase diagram that has not been studied previously. Our work provides a new and practical way to explore the QAH effect in monolayer graphene and the magnetic topological phases by the flexibility of MBT family materials.

Induced superconducting correlations in a quantum anomalous Hall insulator

Thin films of ferromagnetic topological insulator materials can host the quantum anomalous Hall effect without the need for an external magnetic field. Inducing Cooper pairing in such a material is a promising way to realize topological superconductivity with the associated chiral Majorana edge states. However, finding evidence of the superconducting proximity effect in such a state has remained a considerable challenge due to inherent experimental difficulties. Here we demonstrate crossed Andreev reflection across a narrow superconducting Nb electrode that is in contact with the chiral edge state of a quantum anomalous Hall insulator. In the crossed Andreev reflection process, an electron injected from one terminal is reflected out as a hole at the other terminal to form a Cooper pair in the superconductor. This is a compelling signature of induced superconducting pair correlation in the chiral edge state. The characteristic length of the crossed Andreev reflection process is found to be much longer than the superconducting coherence length in Nb, which suggests that the crossed Andreev reflection is, indeed, mediated by superconductivity induced on the quantum anomalous Hall insulator surface. Our results will invite future studies of topological superconductivity and Majorana physics, as well as for the search for non-abelian zero modes.

Even-Odd Layer-Dependent Exchange Bias Effect in MnBi2Te4 Chern Insulator Devices

Magnetic topological materials with coexisting magnetism and nontrivial band structures exhibit many novel quantum phenomena, including the quantum anomalous Hall effect, the axion insulator state, and the Weyl semimetal phase. As a stoichiometric layered antiferromagnetic topological insulator, thin films of MnBi2Te4 show fascinating even-odd layer-dependent physics. In this work, we fabricate a series of thin-flake MnBi2Te4 devices using stencil masks and observe the Chern insulator state at high magnetic fields. Upon magnetic field training, a large exchange bias effect is observed in odd but not in even septuple layer (SL) devices. Through theoretical calculations, we attribute the even-odd layer-dependent exchange bias effect to the contrasting surface and bulk magnetic properties of MnBi2Te4 devices. Our findings reveal the microscopic magnetic configuration of MnBi2Te4 thin flakes and highlight the challenges in replicating the zero magnetic field quantum anomalous Hall effect in odd SL MnBi2Te4 devices.

Engineering Plateau Phase Transition in Quantum Anomalous Hall Multilayers

The plateau phase transition in quantum anomalous Hall (QAH) insulators corresponds to a quantum state wherein a single magnetic domain gives way to multiple domains and then reconverges back to a single magnetic domain. The layer structure of the sample provides an external knob for adjusting the Chern number C of the QAH insulators. Here, we employ molecular beam epitaxy to grow magnetic topological insulator multilayers and realize the magnetic field-driven plateau phase transition between two QAH states with odd Chern number change ΔC. We find that critical exponents extracted for the plateau phase transitions with ΔC = 1 and ΔC = 3 in QAH insulators are nearly identical. We construct a four-layer Chalker-Coddington network model to understand the consistent critical exponents for the plateau phase transitions with ΔC = 1 and ΔC = 3. This work will motivate further investigations into the critical behaviors of plateau phase transitions with different ΔC in QAH insulators.

Sublattice Structure and Topology in Spontaneously Crystallized Electronic States

The prediction and realization of the quantum anomalous Hall effect are often intimately connected to honeycomb lattices in which the sublattice degree of freedom plays a central role in the nontrivial topology. Two-dimensional Wigner crystals, on the other hand, form triangular lattices without sublattice degrees of freedom, resulting in a topologically trivial state. Here, we discuss the possibility of spontaneously formed honeycomb-lattice crystals that exhibit the quantum anomalous Hall effect. Starting from a single-band system with nontrivial quantum geometry, we derive the mean-field energy functional of a class of crystal states and express it as a model of sublattice pseudospins in momentum space. We find that nontrivial quantum geometry leads to extra terms in the pseudospin model that break an effective "time-reversal symmetry" and favor a topologically nontrivial pseudospin texture. When the effects of these extra terms dominate over the ferromagnetic exchange coupling between pseudospins, the anomalous Hall crystal state becomes energetically favorable over the trivial Wigner crystal state.

Imaging the Breakdown and Restoration of Topological Protection in Magnetic Topological Insulator MnBi2Te4

Quantum anomalous Hall (QAH) insulators transport charge without resistance along topologically protected chiral 1D edge states. Yet, in magnetic topological insulators to date, topological protection is far from robust, with zero-magnetic field QAH effect only realized at temperatures an order of magnitude below the Néel temperature TN, though small magnetic fields can stabilize QAH effect. Understanding why topological protection breaks down is therefore essential to realizing QAH effect at higher temperatures. Here a scanning tunneling microscope is used to directly map the size of exchange gap (Eg,ex) and its spatial fluctuation in the QAH insulator 5-layer MnBi2Te4. Long-range fluctuations of Eg,ex are observed, with values ranging between 0 (gapless) and 70 meV, appearing to be uncorrelated to individual surface point defects. The breakdown of topological protection is directly imaged, showing that the gapless edge state, the hallmark signature of a QAH insulator, hybridizes with extended gapless regions in the bulk. Finally, it is unambiguously demonstrated that the gapless regions originate from magnetic disorder, by demonstrating that a small magnetic field restores Eg,ex in these regions, explaining the recovery of topological protection in magnetic fields. The results indicate that overcoming magnetic disorder is the key to exploiting the unique properties of QAH insulators.

Monolayer V_{2}MX_{4}: A New Family of Quantum Anomalous Hall Insulators

We theoretically propose that the van der Waals layered ternary transition metal chalcogenide V_{2}MX_{4} (M=W, Mo; X=S, Se) is a new family of quantum anomalous Hall insulators with sizable bulk gap and Chern number C=-1. The large topological gap originates from the deep band inversion between spin-up bands contributed by d_{xz}, d_{yz} orbitals of V and spin-down band from d_{z^{2}} orbital of M at the Fermi level. Remarkably, the Curie temperature of monolayer V_{2}MX_{4} is predicted to be much higher than that of monolayer MnBi_{2}Te_{4}. Furthermore, the thickness dependence of the Chern number for few multilayers shows interesting oscillating behavior. The general physics from the d orbitals here applies to a large class of ternary transition metal chalcogenide such as Ti_{2}WX_{4} with the space group P-42m. These interesting predictions, if realized experimentally, could greatly promote the research and application of topological quantum physics.

Orbital-Selectivity-Induced Robust Quantum Anomalous Hall Effect in Hund's Metals MgFeP

Ferromagnetic (FM) states with high Curie temperatures (Tc) and strong spin-orbit coupling (SOC) are indispensable for the long-sought room-temperature quantum anomalous Hall (QAH) effects. Here, we propose a two-dimensional (2D) iron-based monolayer MgFeP that exhibits a notably high FM Tc (about 1525 K) along with exceptional structural stabilities. The unique multiorbital nature in MgFeP, where localized d x 2 - y 2 and dxz/yz orbitals coexist with itinerant dxy and dz2 orbitals, renders the monolayer a Hund's metal and in an orbital-selective Mott phase (OSMP). This OSMP triggers an FM double exchange mechanism, rationalizing the high Tc in the Hund's metal. This material transitions to a QAH insulator upon consideration of the SOC effect. By leveraging orbital selectivity, the QAH band gap can be enlarged by more than two times (to 137 meV). Our findings showcase Hund's metals as a promising material platform for realizing high-performance quantum topological electronic devices.

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.

Magneto-optical Effects of an Artificially Layered Ferromagnetic Topological Insulator with a TC of 160 K

Magnetic topological insulators are a fertile platform for studying the interplay between magnetism and topology. The unique electronic band structure can induce exotic transport and optical properties. However, a comprehensive optical study at both near-infrared and terahertz frequencies has been lacking. Here, we report magneto-optical effects from a heterostructure of a Cr-incorporated topological insulator, CBST. By measuring the magneto-optical Kerr effect, we observe a high temperature ferromagnetic transition (160 K) in the CBST film. We also use time-domain terahertz polarimetry to reveal a terahertz Faraday rotation of 1.5 mrad and a terahertz Kerr rotation of 3.6 mrad at 2 K. The calculated terahertz Hall conductance is 0.42 e2/h. Our work shows the optical responses of an artificially layered magnetic topological insulator, paving the way toward a high-temperature quantum anomalous Hall effect via heterostructure engineering.

Gate-tunable Intrinsic Anomalous Hall Effect in Epitaxial MnBi2Te4 Films

The anomalous Hall effect (AHE) is an important transport signature revealing topological properties of magnetic materials and their spin textures. Recently, MnBi2Te4 has been demonstrated to be an intrinsic magnetic topological insulator. However, the origin of its intriguing AHE behaviors remains elusive. Here, we demonstrate the Berry curvature-dominated intrinsic AHE in wafer-scale MnBi2Te4 films. By applying back-gate voltages, we observe an ambipolar conduction and n-p transition in ∼7-layer MnBi2Te4, where a quadratic relation between the AHE resistance and longitudinal resistance suggests its intrinsic AHE nature. In particular, for ∼3-layer MnBi2Te4, the AHE sign can be tuned from pristine negative to positive. First-principles calculations unveil that such an AHE reversal originated from the competing Berry curvature between oppositely polarized spin-minority-dominated surface states and spin-majority-dominated inner bands. Our results shed light on the underlying physical mechanism of the intrinsic AHE and provide new perspectives for the unconventional sign-tunable AHE.

Electrical switching of the edge current chirality in quantum anomalous Hall insulators

A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin-orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.

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.

3D Quantum Anomalous Hall Effect in Magnetic Topological Insulator Trilayers of Hundred-Nanometer Thickness

Magnetic topological states refer to a class of exotic phases in magnetic materials with the non-trivial topological property determined by magnetic spin configurations. An example of such states is the quantum anomalous Hall (QAH) state, which is a zero magnetic field manifestation of the quantum Hall effect. Current research in this direction focuses on QAH insulators with a thickness of less than 10 nm. Here, molecular beam epitaxy (MBE) is employed to synthesize magnetic TI trilayers with a thickness of up to ≈106 nm. It is found that these samples exhibit well-quantized Hall resistance and vanishing longitudinal resistance at zero magnetic field. By varying the magnetic dopants, gate voltages, temperature, and external magnetic fields, the properties of these thick QAH insulators are examined and the robustness of the 3D QAH effect is demonstrated. The realization of the well-quantized 3D QAH effect indicates that the nonchiral side surface states of the thick magnetic TI trilayers are gapped and thus do not affect the QAH quantization. The 3D QAH insulators of hundred-nanometer thickness provide a promising platform for the exploration of fundamental physics, including axion physics and image magnetic monopole, and the advancement of electronic and spintronic devices to circumvent Moore's law.

Insight into the quantum anomalous Hall states in two-dimensional kagome Cr3Se4 and Fe3S4 monolayers

To realize the quantum anomalous Hall (QAH) effect in two-dimensional (2D) intrinsic magnetic materials, which combines insulating bulk states and metallic edge channel states, is still challenging in experiment. Here, based on first-principles calculations, we predicted two stable kagome-latticed QAH insulators: Cr3Se4 and Fe3S4 monolayers, with the Chern number C = 1. It is found that both structures exhibit a large magnetic anisotropy energy and sizable band gaps, and a topological phase transition from C = -1 to C = 1 occurs when the magnetization orientation changes from the z-axis to the -z-axis. Remarkably, the non-trivial topological properties are robust against biaxial strains of up to ±6%. Furthermore, a variable high Chern number of C = 2 or C = 3 can be observed by stacking two or three layers of the QAH monolayer with an MoS2 insulator. Our results signify that such layered kagome materials can be promising platforms for exploring novel QAH physics.

Axion insulator state in hundred-nanometer-thick magnetic topological insulator sandwich heterostructures

An axion insulator is a three-dimensional (3D) topological insulator (TI), in which the bulk maintains the time-reversal symmetry or inversion symmetry but the surface states are gapped by surface magnetization. The axion insulator state has been observed in molecular beam epitaxy (MBE)-grown magnetically doped TI sandwiches and exfoliated intrinsic magnetic TI MnBi2Te4 flakes with an even number layer. All these samples have a thickness of ~ 10 nm, near the 2D-to-3D boundary. The coupling between the top and bottom surface states in thin samples may hinder the observation of quantized topological magnetoelectric response. Here, we employ MBE to synthesize magnetic TI sandwich heterostructures and find that the axion insulator state persists in a 3D sample with a thickness of ~ 106 nm. Our transport results show that the axion insulator state starts to emerge when the thickness of the middle undoped TI layer is greater than ~ 3 nm. The 3D hundred-nanometer-thick axion insulator provides a promising platform for the exploration of the topological magnetoelectric effect and other emergent magnetic topological states, such as the high-order TI phase.

Quantum-anomalous-Hall current patterns and interference in thin slabs of chiral topological superconductors

The chiral topological superconductor, which supports propagating nontrivial edge modes while maintaining a gapped bulk, can be realized hybridizing a quantum-anomalous-Hall thin slab with an ordinary s-wave superconductor. We show that by sweeping the voltage bias in a normal-hybrid-normal double junction, the pattern of electric currents in the normal leads spans three main regimes. From single-mode edge-current quantization at low bias, to double-mode edge-current oscillations at intermediate voltages and up to diffusive bulk currents at larger voltages. Observing such patterns by resolving the spatial distribution of the local current in the thin slab could provide additional evidence, besides the global conductance, on the physics of chiral topological superconductors.

Quantum anomalous valley Hall effect in ferromagnetic MXenes with asymmetric functionalization

The potential to detect and manipulate the valley degree of freedom within two-dimensional hexagonal lattices possessing both inversion asymmetry and time-reversal symmetry is theoretically feasible. Intrinsic ferrovalley polarization in MXenes could be induced by asymmetric surface functionalization to break their inversion symmetry and the presence of spin-orbital coupling ensures their time-reversal symmetry. Our results indicate that the ferromagnetic Cr2COF MXene with Janus functionalization becomes an intrinsic Chern insulator with large spin-valley polarization and belongs to the family of quantum anomalous valley Hall effect (QAVHE) materials, based on Berry curvature and edge state calculations. Applying chemical engineering of functionalization to magnetic MXenes allows us to tune the structure-property relationship in 2D layers to obtain desirable spin-valley coupling. Our theoretical insight into the QAVHE on magnetic MXenes with asymmetry functionalization provides a new opportunity for valleytronics and spintronics.

Strain-tunable magnetism and topological states in layered VBi2Te4

Similar to the magnetic topological insulator of MnBi2Te4, recent studies have demonstrated that VBi2Te4 is also an ideal candidate to explore many intriguing quantum states. Different from the strong interlayer antiferromagnetic (AFM) coupling in layered MnBi2Te4, based on first-principles calculations, we find that the energy difference between AFM and ferromagnetic (FM) orders in layered VBi2Te4 is much smaller than that of MnBi2Te4. Specifically, it is found that the interlayer FM coupling can be readily achieved by applying strain. Further electronic band structures reveal that the VBi2Te4 bilayer is a time-reversal symmetry broken quantum spin Hall insulator with a spin Chern number of CS = 1, which is essentially different from the QAH state with a Chern number of C = 1 in the MnBi2Te4 bilayer. Most strikingly, the topological states of the magnetic VBi2Te4 bilayer can be well tuned by strain, whose topological phase diagram is mapped out as a function of strain by employing continuum model analyses. All of these results indicate that the layered VBi2Te4 not only enriches the family of magnetic topological materials, but also provides a promising platform to explore more exotic quantum phenomena.

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.

Manipulating Topological Phases in Magnetic Topological Insulators

Magnetic topological insulators (MTIs) are a group of materials that feature topological band structures with concurrent magnetism, which can offer new opportunities for technological advancements in various applications, such as spintronics and quantum computing. The combination of topology and magnetism introduces a rich spectrum of topological phases in MTIs, which can be controllably manipulated by tuning material parameters such as doping profiles, interfacial proximity effect, or external conditions such as pressure and electric field. In this paper, we first review the mainstream MTI material platforms where the quantum anomalous Hall effect can be achieved, along with other exotic topological phases in MTIs. We then focus on highlighting recent developments in modulating topological properties in MTI with finite-size limit, pressure, electric field, and magnetic proximity effect. The manipulation of topological phases in MTIs provides an exciting avenue for advancing both fundamental research and practical applications. As this field continues to develop, further investigations into the interplay between topology and magnetism in MTIs will undoubtedly pave the way for innovative breakthroughs in the fundamental understanding of topological physics as well as practical applications.

Quantized resistance revealed at the criticality of the quantum anomalous Hall phase transitions

In multilayered magnetic topological insulator structures, magnetization reversal processes can drive topological phase transitions between quantum anomalous Hall, axion insulator, and normal insulator states. Here we report an examination of the critical behavior of two such transitions: the quantum anomalous Hall to normal insulator (QAH-NI), and quantum anomalous Hall to axion insulator (QAH-AXI) transitions. By introducing a new analysis protocol wherein temperature dependent variations in the magnetic coercivity are accounted for, the critical behavior of the QAH-NI and QAH-AXI transitions are evaluated over a wide range of temperature and magnetic field. Despite the uniqueness of these different transitions, quantized longitudinal resistance and Hall conductance are observed at criticality in both cases. Furthermore, critical exponents were extracted for QAH-AXI transitions occurring at magnetization reversals of two different magnetic layers. The observation of consistent critical exponents and resistances in each case, independent of the magnetic layer details, demonstrates critical behaviors in quantum anomalous Hall transitions to be of electronic rather than magnetic origin. Our finding offers a new avenue for studies of phase transition and criticality in QAH insulators.

Hunting for Majoranas

Over the past decade, there have been considerable efforts to observe non-abelian quasiparticles in novel quantum materials and devices. These efforts are motivated by the goals of demonstrating quantum statistics of quasiparticles beyond those of fermions and bosons and of establishing the underlying science for the creation of topologically protected quantum bits. In this Review, we focus on efforts to create topological superconducting phases that host Majorana zero modes. We consider the lessons learned from existing experimental efforts, which are motivating both improvements to present platforms and the exploration of new approaches. Although the experimental detection of non-abelian quasiparticles remains challenging, the knowledge gained thus far and the opportunities ahead offer high potential for discovery and advances in this exciting area of quantum physics.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

General nonlinear Hall current in magnetic insulators beyond the quantum anomalous Hall effect

Can a generic magnetic insulator exhibit a Hall current? The quantum anomalous Hall effect (QAHE) is one example of an insulating bulk carrying a quantized Hall conductivity while insulators with zero Chern number present zero Hall conductance in the linear response regime. Here, we find that a general magnetic insulator possesses a nonlinear Hall conductivity quadratic to the electric field if the system breaks inversion symmetry, which can be identified as a new type of multiferroic coupling. This conductivity originates from an induced orbital magnetization due to virtual interband transitions. We identify three contributions to the wavepacket motion, a velocity shift, a positional shift, and a Berry curvature renormalization. In contrast to the crystalline solid, we find that this nonlinear Hall conductivity vanishes for Landau levels of a 2D electron gas, indicating a fundamental difference between the QAHE and the integer quantum Hall effect.

Giant nonlocal edge conduction in the axion insulator state of MnBi2Te4

The recently discovered antiferromagnetic (AFM) topological insulator (TI) MnBi₂Te₄ represents a versatile material platform for exploring exotic topological quantum phenomena in nanoscale devices. It has been proposed that even-septuple-layer (even-SL) MnBi₂Te₄ can host helical hinge currents with unique nonlocal behavior, but experimental confirmation is still lacking. In this work, we report transport studies of exfoliated MnBi₂Te₄ flakes with varied thicknesses down to the few-nanometer regime. We observe giant nonlocal transport signals in even-SL devices when the system is in the axion insulator state but vanishingly small nonlocal signal in the odd-SL devices at the same magnetic field range. In conjunction with theoretical calculations, we demonstrate that the nonlocal transport is via the helical edge currents mainly distributed at the hinges between the side and top/bottom surfaces. The helical edge currents in the axion insulator state may find unique applications in topological quantum devices.

Experimental Demonstration of a Magnetically Induced Warping Transition in a Topological Insulator Mediated by Rare-Earth Surface Dopants

Magnetic topological insulators constitute a novel class of materials whose topological surface states (TSSs) coexist with long-range ferromagnetic order, eventually breaking time-reversal symmetry. The subsequent bandgap opening is predicted to co-occur with a distortion of the TSS warped shape from hexagonal to trigonal. We demonstrate such a transition by means of angle-resolved photoemission spectroscopy on the magnetically rare-earth (Er and Dy) surface-doped topological insulator Bi₂Se₂Te. Signatures of the gap opening are also observed. Moreover, increasing the dopant coverage results in a tunable p-type doping of the TSS, thereby allowing for a gradual tuning of the Fermi level toward the magnetically induced bandgap. A theoretical model where a magnetic Zeeman out-of-plane term is introduced in the Hamiltonian governing the TSS rationalizes these experimental results. Our findings offer new strategies to control magnetic interactions with TSSs and open up viable routes for the realization of the quantum anomalous Hall effect.

Evolution of Dopant-Concentration-Induced Magnetic Exchange Interaction in Topological Insulator Thin Films

To date, the quantum anomalous Hall effect has been realized in chromium (Cr)- and/or vanadium(V)-doped topological insulator (Bi,Sb)₂Te₃ thin films. In this work, we use molecular beam epitaxy to synthesize both V- and Cr-doped Bi₂Te₃ thin films with controlled dopant concentration. By performing magneto-transport measurements, we find that both systems show an unusual yet similar ferromagnetic response with respect to magnetic dopant concentration; specifically the Curie temperature does not increase monotonically but shows a local maximum at a critical dopant concentration. We attribute this unusual ferromagnetic response observed in Cr/V-doped Bi₂Te₃ thin films to the dopant-concentration-induced magnetic exchange interaction, which displays evolution from van Vleck-type ferromagnetism in a nontrivial magnetic topological insulator to Ruderman-Kittel-Kasuya-Yosida (RKKY)-type ferromagnetism in a trivial diluted magnetic semiconductor. Our work provides insights into the ferromagnetic properties of magnetically doped topological insulator thin films and facilitates the pursuit of high-temperature quantum anomalous Hall effect.

Intermixing-Driven Surface and Bulk Ferromagnetism in the Quantum Anomalous Hall Candidate MnBi6 Te10

The recent realizations of the quantum anomalous Hall effect (QAHE) in MnBi₂ Te₄ and MnBi₄ Te₇ benchmark the (MnBi₂ Te₄ )(Bi₂ Te₃ )_n family as a promising hotbed for further QAHE improvements. The family owes its potential to its ferromagnetically (FM) ordered MnBi₂ Te₄ septuple layers (SLs). However, the QAHE realization is complicated in MnBi₂ Te₄ and MnBi₄ Te₇ due to the substantial antiferromagnetic (AFM) coupling between the SLs. An FM state, advantageous for the QAHE, can be stabilized by interlacing the SLs with an increasing number n of Bi₂ Te₃ quintuple layers (QLs). However, the mechanisms driving the FM state and the number of necessary QLs are not understood, and the surface magnetism remains obscure. Here, robust FM properties in MnBi₆ Te₁₀ (n = 2) with T_c ≈ 12 K are demonstrated and their origin is established in the Mn/Bi intermixing phenomenon by a combined experimental and theoretical study. The measurements reveal a magnetically intact surface with a large magnetic moment, and with FM properties similar to the bulk. This investigation thus consolidates the MnBi₆ Te₁₀ system as perspective for the QAHE at elevated temperatures.

Floquet Engineering of Nonequilibrium Valley-Polarized Quantum Anomalous Hall Effect with Tunable Chern Number

Here, we propose that Floquet engineering offers a strategy to realize the nonequilibrium quantum anomalous Hall effect (QAHE) with tunable Chern number. Using first-principles calculations and Floquet theorem, we unveil that QAHE related to valley polarization (VP-QAHE) is formed from the hybridization of Floquet sidebands in the two-dimensional family MSi₂Z₄ (M = Mo, W, V; Z = N, P, As) by irradiating circularly polarized light (CPL). Through the tuning of frequency, intensity, and handedness of CPL, the Chern number of VP-QAHE is highly tunable and up to C = ±4, which attributes to light-induced trigonal warping and multiple-band inversion at different valleys. The chiral edge states and quantized plateau of Hall conductance are visible inside the global band gap, thereby facilitating the experimental measurement. Our work not only establishes Floquet engineering of nonequilibrium VP-QAHE with tunable Chern number in realistic materials but also provides an avenue to explore emergent topological phases under light irradiation.

Realization of quasi-1D topological magnetism at the V-alloyed MoS2 zigzag edge

Topological magnetism in quasi-1D systems can be interesting because of the significant quantum confinement. However, the realization is missing. In this letter, we propose the use of 3× periodicities related edge reconstructions of MoS₂ zigzag edges to construct a topological quasi-1D spin chain. Specifically, a trimer Su-Schrieffer-Heeger model can be applied to illustrate the topological and spin order when the inter-cell hopping integral is larger than the intra-cell ones. As a result, topological ferromagnetic order is achieved for S-oriented edge states magnetized by V atoms and confirmed by first-principles calculations and Wannier functions analysis. Finally, gap opening and spin-polarized end states are realized.

Electrically Tunable Topological Phase Transition in van der Waals Heterostructures

The realization and control of the quantum anomalous Hall (QAH) effect are highly desirable for the development of spintronic and quantum devices. In this work, we propose a van der Waals (vdW) heterostructure of ultrathin MnBi₂Se₄ and Bi₂Se₃ layers and demonstrate that it is an excellent tunable QAH platform by using model Hamiltonian and density functional theory simulations. Its band gap closes and reopens as external electric field increases, manifesting a novel topological phase transition with an electric field of ∼0.06 V/Å. This heterostructure has other major advantageous, such as large topological band gap, perpendicular magnetization, and strong ferromagnetic ordering. Our work provides clear physical insights and suggests a new strategy for experimental realization and control of the QAH effect in real materials.

Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional (1D) conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the 1D edges and exponentially decay in the two-dimensional (2D) bulk. In this Letter, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths under gate voltages. At the charge neutral point, the QAH effect persists in a Hall bar device with a width of only ∼72  nm, implying the intrinsic decaying length of CECs is less than ∼36  nm. In the electron-doped regime, we find that the Hall resistance deviates quickly from the quantized value when the sample width is less than 1  μm. Our theoretical calculations suggest that the wave function of CEC first decays exponentially and then shows a long tail due to disorder-induced bulk states. Therefore, the deviation from the quantized Hall resistance in narrow QAH samples originates from the interaction between two opposite CECs mediated by disorder-induced bulk states in QAH insulators, consistent with our experimental observations.

Creation of chiral interface channels for quantized transport in magnetic topological insulator multilayer heterostructures

One-dimensional chiral interface channels can be created at the boundary of two quantum anomalous Hall (QAH) insulators with different Chern numbers. Such a QAH junction may function as a chiral edge current distributer at zero magnetic field, but its realization remains challenging. Here, by employing an in-situ mechanical mask, we use molecular beam epitaxy to synthesize QAH insulator junctions, in which two QAH insulators with different Chern numbers are connected along a one-dimensional junction. For the junction between Chern numbers of 1 and -1, we observe quantized transport and demonstrate the appearance of the two parallel propagating chiral interface channels along the magnetic domain wall at zero magnetic field. For the junction between Chern numbers of 1 and 2, our quantized transport shows that a single chiral interface channel appears at the interface. Our work lays the foundation for the development of QAH insulator-based electronic and spintronic devices and topological chiral networks.

Topological Phase Transitions Driven by Sn Doping in (Mn1−xSnx)Bi2Te4

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 its topologically nontrivial nature and a number of fundamental phenomena. At the same time, the possibility to control the electronic and magnetic properties of this system can provide new effective ways for its application in devices. One of the approaches to manipulate MnBi2Te4 properties is the partial substitution of magnetic atoms in the compound with atoms of non-magnetic elements, which inevitably affect the interplay of magnetism and band topology in the system. In this work, we have carried out theoretical modelling of changes in the electronic structure that occur as a result of increasing the concentration of Sn atoms at Mn positions in the (Mn1−xSnx)Bi2Te4 compound both using Korringa–Kohn–Rostoker (KKR) Green’s function method as well as the widespread approach of using supercells with impurity in DFT methods. The calculated band structures were also compared with those experimentally measured by angle-resolved photoelectron spectroscopy (ARPES) for samples with x values of 0, 0.19, 0.36, 0.52 and 0.86. We assume that the complex hybridization of Te-pz and Bi-pz orbitals with Sn and Mn ones leads to a non-linear dependence of band gap on Sn content in Mn positions, which is characterized by a plateau with a zero energy gap at some concentration values, suggesting possible topological phase transitions in the system.

Environmental Doping-Induced Degradation of the Quantum Anomalous Hall Insulators

The quantum anomalous Hall (QAH) insulator carries dissipation-free chiral edge current and thus provides a unique opportunity to develop energy-efficient transformative information technology. Despite promising advances, the QAH insulator has thus far eluded any practical applications. In addition to its low working temperature, the QAH state in magnetically doped topological insulators usually deteriorates with time in ambient conditions. In this work, we store three QAH devices with similar initial properties in different environments. The QAH device without a protection layer in air shows clear degradation and becomes hole-doped. The QAH device kept in an argon glovebox without a protection layer shows no measurable degradation after 560 h, and the device protected by a 3 nm AlO_x protection layer in air shows minimal degradation with stable QAH properties. Our work shows a route to preserve the dissipation-free chiral edge state in QAH devices for potential applications in quantum information technology.

Robust Interlayer-Coherent Quantum Hall States in Twisted Bilayer Graphene

We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely, twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, sub-nanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau level (N = 1). Notably the energy gaps for these states are of order 1 K, which is several orders of magnitude greater than those in GaAs. Furthermore, a variety of quantum Hall phase transitions are observed experimentally. All the experimental observations are largely consistent with our phenomenological model calculations. Hence, we establish that a large twist angle system is an excellent platform for high-temperature excitonic condensation.

Controllable Chirality and Band Gap of Quantum Anomalous Hall Insulators

Finding guiding principles to optimize properties of quantum anomalous Hall (QAH) insulators is of pivotal importance to fundamental science and applications. Here, we build a first-principles QAH material database of chirality and band gap, explore microscopic mechanisms determining the QAH material properties, and obtain a general physical picture that can help researchers comprehensively understand the QAH data. Our results reveal that the usually neglected Coulomb exchange is unexpectedly strong in a large class of QAH materials, which is the key to resolve experimental puzzles. Moreover, we identify simple indicators for property evaluation and suggest material design strategies to control QAH chirality and gap by tuning cooperative or competing contributions via magnetic codoping, heterostructuring, spin-orbit proximity, etc. The work is valuable to future research of magnetic topological physics and materials.

Direct visualization of edge state in even-layer MnBi2Te4 at zero magnetic field

Being the first intrinsic antiferromagnetic (AFM) topological insulator (TI), MnBi2Te4 is argued to be a topological axion state in its even-layer form due to the antiparallel magnetization between the top and bottom layers. Here we combine both transport and scanning microwave impedance microscopy (sMIM) to investigate such axion state in atomically thin MnBi2Te4 with even-layer thickness at zero magnetic field. While transport measurements show a zero Hall plateau signaturing the axion state, sMIM uncovers an unexpected edge state raising questions regarding the nature of the "axion state". Based on our model calculation, we propose that the edge state of even-layer MnBi2Te4 at zero field is derived from gapped helical edge states of the quantum spin Hall effect with time-reversal-symmetry breaking, when a crossover from a three-dimensional TI MnBi2Te4 to a two-dimensional TI occurs. Our finding thus signifies the richness of topological phases in MnB2Te4 that has yet to be fully explored.

Highly Tunable Beyond-Room-Temperature Intrinsic Ferromagnetism in Cr-Doped Topological Crystalline Insulator SnTe Crystals

The combination of topological phase and intrinsic beyond-room-temperature ferromagnetism is expected to realize the quantum anomalous Hall effect at a high temperature. However, no beyond-room-temperature intrinsic ferromagnetism has been reported in either topological insulator or topological crystalline insulator (TCI) so far. Here, we report Cr-doping in TCI-phase SnTe crystals which possess highly tunable beyond-room-temperature intrinsic ferromagnetism including T_c, magnetic moment, and coercivity by varying Cr contents and crystal thickness. With the increase of the Cr content, the T_c increases by 159 K from 221 to 380 K and the saturation magnetic moments increase by ∼23.6 times from 0.018 to 0.421 μ_B/f.u. This intrinsic beyond-room-temperature ferromagnetism is fully demonstrated by the anomalous Hall effect and magneto-optical Kerr effect in a single Cr_xSn_1-xTe nanosheet. Moreover, the room-temperature tunneling magnetoresistance effect has been realized by using a Cr_xSn_1-xTe flake, a Fe thin film, and a commercially compatible ultrathin AlO_x tunneling barrier. This work indicates a great potential of Cr_xSn_1-xTe crystals in room-temperature magnetoelectronic and spintronic devices.

Measured Potential Profile in a Quantum Anomalous Hall System Suggests Bulk-Dominated Current Flow

Ideally, quantum anomalous Hall systems should display zero longitudinal resistance. Yet in experimental quantum anomalous Hall systems elevated temperature can make the longitudinal resistance finite, indicating dissipative flow of electrons. Here, we show that the measured potentials at multiple locations within a device at elevated temperature are well described by solution of Laplace's equation, assuming spatially uniform conductivity, suggesting nonequilibrium current flows through the two-dimensional bulk. Extrapolation suggests that at even lower temperatures current may still flow primarily through the bulk rather than, as had been assumed, through edge modes. An argument for bulk current flow previously applied to quantum Hall systems supports this picture.

Probing the mesoscopic size limit of quantum anomalous Hall insulators

The inelastic scattering length (L_s) is a length scale of fundamental importance in condensed matters due to the relationship between inelastic scattering and quantum dephasing. In quantum anomalous Hall (QAH) materials, the mesoscopic length scale L_s plays an instrumental role in determining transport properties. Here we examine L_s in three regimes of the QAH system with distinct transport behaviors: the QAH, quantum critical, and insulating regimes. Although the resistance changes by five orders of magnitude when tuning between these distinct electronic phases, scaling analyses indicate a universal L_s among all regimes. Finally, mesoscopic scaled devices with sizes on the order of L_s were fabricated, enabling the direct detection of the value of L_s in QAH samples. Our results unveil the fundamental length scale that governs the transport behavior of QAH materials.

In quantum anomalous Hall (QAH) materials, the mesoscopic scattering length (L_s) plays an instrumental role in determining transport properties. Here, the authors examine L_s in three regimes (QAH, quantum critical, and insulating) with distinct transport behaviours, and find a universal L_s across all regimes.

Intrinsic Magnetic (EuIn)As Nanowire Shells with a Unique Crystal Structure

In the pursuit of magneto-electronic systems nonstoichiometric magnetic elements commonly introduce disorder and enhance magnetic scattering. We demonstrate the growth of (EuIn)As shells, with a unique crystal structure comprised of a dense net of Eu inversion planes, over InAs and InAs_1-xSb_x core nanowires. This is imaged with atomic and elemental resolution which reveal a prismatic configuration of the Eu planes. The results are supported by molecular dynamics simulations. Local magnetic and susceptibility mappings show magnetic response in all nanowires, while a subset bearing a DC signal points to ferromagnetic order. These provide a mechanism for enhancing Zeeman responses, operational at zero applied magnetic field. Such properties suggest that the obtained structures can serve as a preferred platform for time-reversal symmetry broken one-dimensional states including intrinsic topological superconductivity.

Structural Defects and Ferromagnetic Signature of V-Doped Sb2Te3 Thin Films Grown on SrTiO3(001) Produced by RF-Magnetron Sputtering

Thin films of V-doped Sb₂Te₃ compounds were fabricated by co-deposition of Sb₂Te₃ and V using rf-magnetron sputtering onto SrTiO₃(001) substrates kept at 570 K. The microstructures of the films were characterized using transmission electron microscopy (TEM) and electron diffraction. The crystal structure of the sputtered film (Sb₃₈V₂Te₆₀) is the Bi₂Te₃-type structure with lattice parameters of a = 0.44 ± 0.03 nm and c = 3.02 ± 0.02 nm. A combination of cross-sectional and plan-view TEM observations revealed the preferential orientation of the c axis in the film's normal direction. A thin amorphous layer exists between the Sb₂Te₃ thin film and the SrTiO₃ substrate. The interfacial amorphous layer relaxes the strain between the thin film and the substrate, and hence, it should promote the growth of a low-index atomic plane with a low surface free energy (i.e., (0001) of the Sb₂Te₃). The onset of ferromagnetic order was detected at temperatures below 70 K. A remarkable increase in magnetization was detected in the film's normal direction, which corresponds to the magnetic easy axis (i.e., c axis of the Sb₂Te₃). V³⁺ ions substituting Sb sites should contribute to ferromagnetism at low temperatures.

Two-Dimensional Van Der Waals Topological Materials: Preparation, Properties, and Device Applications

Over the past decade, 2D van der Waals (vdW) topological materials (TMs), including topological insulators and topological semimetals, which combine atomically flat 2D layers and topologically nontrivial band structures, have attracted increasing attention in condensed-matter physics and materials science. These easily cleavable and integrated TMs provide the ideal platform for exploring topological physics in the 2D limit, where new physical phenomena may emerge, and represent a potential to control and investigate exotic properties and device applications in nanoscale topological phases. However, multifaced efforts are still necessary, which is the prerequisite for the practical application of 2D vdW TMs. Herein, this review focuses on the preparation, properties, and device applications of 2D vdW TMs. First, three common preparation strategies for 2D vdW TMs are summarized, including single crystal exfoliation, chemical vapor deposition, and molecular beam epitaxy. Second, the origin and regulation of various properties of 2D vdW TMs are introduced, involving electronic properties, transport properties, optoelectronic properties, thermoelectricity, ferroelectricity, and magnetism. Third, some device applications of 2D vdW TMs are presented, including field-effect transistors, memories, spintronic devices, and photodetectors. Finally, some significant challenges and opportunities for the practical application of 2D vdW TMs in 2D topological electronics are briefly addressed.

Two-dimensional antiferromagnetic nodal-line semimetal and quantum anomalous Hall state in the van der Waals heterostructure germanene/Mn2S2

Materials with interactions between the topology and magnetism are triggering increasing interest. We constructed a two-dimensional (2D) van der Waals heterostructure germanene/Mn₂S₂, where the germanene is a quantum spin Hall insulator and Mn₂S₂provides antiferromagnetic (AFM) interactions. In this structure, a 2D AFM nodal-line semimetal (NLSM) phase is expected without the spin-orbit coupling (SOC), which is of a high density of states around the Fermi level. The band touching rings originate from the intersection between different spin components ofporbitals of germanene. This result provides a possible 2D realization of NLSMs, which are usually realized in three-dimensional systems. When the SOC is present, a quantum anomalous Hall (QAH) state emerges with the annihilation of the band-touching rings. The nontrivial topology is determined by calculating the Chern number and Wannier charge centers. This provides an alternative platform to realize QAH states. These results could also provide the possibility of further understanding the topological states in NLSM and electronic applications.

High-Temperature Quantum Hall Effect in Graphite-Gated Graphene Heterostructure Devices with High Carrier Mobility

Since the discovery of the quantum Hall effect in 1980, it has attracted intense interest in condensed matter physics and has led to a new type of metrological standard by utilizing the resistance quantum. Graphene, a true two-dimensional electron gas material, has demonstrated the half-integer quantum Hall effect and composite-fermion fractional quantum Hall effect due to its unique massless Dirac fermions and ultra-high carrier mobility. Here, we use a monolayer graphene encapsulated with hexagonal boron nitride and few-layer graphite to fabricate micrometer-scale graphene Hall devices. The application of a graphite gate electrode significantly screens the phonon scattering from a conventional SiO2/Si substrate, and thus enhances the carrier mobility of graphene. At a low temperature, the carrier mobility of graphene devices can reach 3 × 105 cm2/V·s, and at room temperature, the carrier mobility can still exceed 1 × 105 cm2/V·s, which is very helpful for the development of high-temperature quantum Hall effects under moderate magnetic fields. At a low temperature of 1.6 K, a series of half-integer quantum Hall plateaus are well-observed in graphene with a magnetic field of 1 T. More importantly, the ν = ±2 quantum Hall plateau clearly persists up to 150 K with only a few-tesla magnetic field. These findings show that graphite-gated high-mobility graphene devices hold great potential for high-sensitivity Hall sensors and resistance metrology standards for the new Système International d'unités.