Metal-to-insulator switching in quantum anomalous Hall states

Conformity Experiment on Inelastic Scattering Exponent of Electrons in Two Dimensions

The quantum Hall (QH) effect is one of the most widely studied physical phenomenon in two dimensions. The plateau-plateau transition within this effect can be comprehensively described by the scaling theory, which encompasses three pivotal exponents: the critical exponent κ, the inelastic scattering exponent p, and the universal exponent γ. Prior studies have focused on measuring κ and estimating γ, assuming a constant p value of 2 across magnetic fields. Here, our work marks a significant advancement by measuring all three exponents within a single graphene device and a conventional two-dimensional electron system. This study uniquely determines p at low magnetic fields (weak localization region and well outside the QH regime) and high magnetic fields (in the vicinity of the QH regime). Employing a comprehensive analytical approach that includes weak localization, plateau-plateau transitions, and variable range hopping, we have directly determined κ, p, and γ. Our findings reveal a distinct variation in p, shifting from 1 in the low magnetic field regime to 2 in the QH regime in graphene.

Antiferromagnetic Chern insulator with large charge gap in heavy transition-metal compounds

Despite the discovery of multiple intrinsic magnetic topological insulators in recent years the observation of Chern insulators is still restricted to very low temperatures due to the negligible charge gaps. Here, we uncover the potential of heavy transition-metal compounds for realizing a collinear antiferromagnetic Chern insulator (AFCI) with a charge gap as large as 300 meV. Our analysis relies on the Kane-Mele-Kondo model with a ferromagnetic Hund coupling J H between the spins of itinerant electrons and the localized spins of size S. We show that a spin-orbit couplingλ SO ≳ 0.03 t , where t is the nearest-neighbor hopping element, is already large enough to stabilize an AFCI provided the alternating sublattice potential δ is in the range δ ≈ S J H . We establish a remarkable increase in the charge gap upon increasing λ SO in the AFCI phase. Using our results we explain the collinear AFCI recently found in monolayers of CrO and MoO with charge gaps of 1 and 50 meV , respectively. In addition, we propose bilayers of heavy transition-metal oxides of perovskite structure as candidates to realize a room-temperature AFCI if grown along the [111] direction and subjected to a perpendicular electric field.

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.

Topological magnetoelectric response in ferromagnetic axion insulators

The topological magnetoelectric effect (TME) is a hallmark response of the topological field theory, which provides a paradigm shift in the study of emergent topological phenomena. However, its direct observation is yet to be realized due to the demanding magnetic configuration required to gap all surface states. Here, we theoretically propose that axion insulators with a simple ferromagnetic configuration, such as the MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize the TME. In the designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical electric field, the surface Hall currents give rise to a nearly half-quantized orbital moment, accompanied by a gapless chiral hinge mode circulating in parallel. Thus, the orbital magnetization from the two topological origins can be easily distinguished by reversing the electric field. Our work paves the way for direct observation of the TME in realistic axion-insulator materials.

Quantized anomalous Hall resistivity achieved in molecular beam epitaxy-grown MnBi2Te4 thin films

The intrinsic magnetic topological insulator MnBi2Te4 provides a feasible pathway to the high-temperature quantum anomalous Hall (QAH) effect as well as various novel topological quantum phases. Although quantized transport properties have been observed in exfoliated MnBi2Te4 thin flakes, it remains a big challenge to achieve molecular beam epitaxy (MBE)-grown MnBi2Te4 thin films even close to the quantized regime. In this work, we report the realization of quantized anomalous Hall resistivity in MBE-grown MnBi2Te4 thin films with the chemical potential tuned by both controlled in situ oxygen exposure and top gating. We find that elongated post-annealing obviously elevates the temperature to achieve quantization of the Hall resistivity, but also increases the residual longitudinal resistivity, indicating a picture of high-quality QAH puddles weakly coupled by tunnel barriers. These results help to clarify the puzzles in previous experimental studies on MnBi2Te4 and to find a way out of the big difficulty in obtaining MnBi2Te4 samples showing quantized transport properties.

Epitaxial Growth and Characterization of Nanoscale Magnetic Topological Insulators: Cr-Doped (Bi0.4Sb0.6)2Te3

The exploration initiated by the discovery of the topological insulator (BixSb1-x)2Te3 has extended to unlock the potential of quantum anomalous Hall effects (QAHEs), marking a revolutionary era for topological quantum devices, low-power electronics, and spintronic applications. In this study, we present the epitaxial growth of Cr-doped (Bi0.4Sb0.6)2Te3 (Cr:BST) thin films via molecular beam epitaxy, incorporating various Cr doping concentrations with varying Cr/Sb ratios (0.025, 0.05, 0.075, and 0.1). High-quality crystalline of the Cr:BST thin films deposited on a c-plane sapphire substrate has been rigorously confirmed through reflection high-energy electron diffraction (RHEED), X-ray diffraction (XRD), and high-resolution transmission electron microscopy (HRTEM) analyses. The existence of a Cr dopant has been identified with a reduction in the lattice parameter of BST from 30.53 ± 0.05 to 30.06 ± 0.04 Å confirmed by X-ray diffraction, and the valence state of Cr verified by X-ray photoemission (XPS) at binding energies of ~573.1 and ~583.5 eV. Additionally, the influence of Cr doping on lattice vibration was qualitatively examined by Raman spectroscopy, revealing a blue shift in peaks with increased Cr concentration. Surface characteristics, crucial for the functionality of topological insulators, were explored via Atomic Force Microscopy (AFM), illustrating a sevenfold reduction in surface roughness as the Cr concentration increased from 0 to 0.1. The ferromagnetic properties of Cr:BST were examined by a superconducting quantum interference device (SQUID) with a magnetic field applied in out-of-plane and in-plane directions. The Cr:BST samples exhibited a Curie temperature (Tc) above 50 K, accompanied by increased magnetization and coercivity with increasing Cr doping levels. The introduction of the Cr dopant induces a transition from n-type ((Bi0.4Sb0.6)2Te3) to p-type (Cr:(Bi0.4Sb0.6)2Te3) carriers, demonstrating a remarkable suppression of carrier density up to one order of magnitude, concurrently enhancing carrier mobility up to a factor of 5. This pivotal outcome is poised to significantly influence the development of QAHE studies and spintronic applications.

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.

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.

Controlling the Zero Hall Plateau in a Quantum Anomalous Hall Insulator by In-Plane Magnetic Field

We investigate the quantum anomalous Hall plateau transition in the presence of independent out-of-plane and in-plane magnetic fields. The perpendicular coercive field, zero Hall plateau width, and peak resistance value can all be systematically controlled by the in-plane magnetic field. The traces taken at various fields almost collapse into a single curve when the field vector is renormalized to an angle as a geometric parameter. These results can be explained consistently by the competition between magnetic anisotropy and in-plane Zeeman field, and the close relationship between quantum transport and magnetic domain structure. The accurate control of zero Hall plateau facilitates the search for chiral Majorana modes based on the quantum anomalous Hall system in proximity to a superconductor.

Electrical Manipulation of Topological Phases in a Quantum Anomalous Hall Insulator

Quantum anomalous Hall phases arising from the inverted band topology in magnetically doped topological insulators have emerged as an important subject of research for quantization at zero magnetic fields. Though necessary for practical implementation, sophisticated electrical control of molecular beam epitaxy (MBE)-grown quantum anomalous Hall matter have been stymied by growth and fabrication challenges. Here, a novel procedure is demonstrated, employing a combination of thin-film deposition and 2D material stacking techniques, to create dual-gated devices of the MBE-grown quantum anomalous Hall insulator, Cr-doped (Bi,Sb)₂ Te₃ . In these devices, orthogonal control over the field-induced charge density and the electric displacement field is demonstrated. A thorough examination of material responses to tuning along each control axis is presented, realizing magnetic property control along the former and a novel capability to manipulate the surface exchange gap along the latter. Through electrically addressing the exchange gap, the capabilities to either strengthen the quantum anomalous Hall state or suppress it entirely and drive a topological phase transition to a trivial state are demonstrated. The experimental result is explained using first principle theoretical calculations, and establishes a practical route for in situ control of quantum anomalous Hall states and topology.

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.

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.

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.

Direct Probe of the Ferromagnetic Proximity Effect at the Interface of SnTe/Fe Heterostructure by Polarized Neutron Reflectometry

Introducing magnetic order into a topological insulator (TI) system has attracted much attention with an expectation of realizing exotic phenomena such as the quantum anomalous Hall effect (QAHE) and axion insulator states. The magnetic proximity effect (MPE) is one of the promising schemes to induce the magnetic order on the surface of a TI without introducing disorder accompanied by doping magnetic impurities in the TI. In this study, we investigate the MPE at the interface of a heterostructure consisting of the topological crystalline insulator (TCI) SnTe and Fe by employing polarized neutron reflectometry. The ferromagnetic order penetrates ∼2.2 nm deep into the SnTe layer from the interface with Fe, which persists up to room temperature. This is induced by the MPE on the surface of the TCI preserving the coherent topological states without introducing the disorder by doping magnetic impurities. This would open up a way for realizing next-generation spintronics and quantum computational devices.

Observation of Magnetism-Induced Topological Edge State in Antiferromagnetic Topological Insulator MnBi4Te7

Breaking time reversal symmetry in a topological insulator may lead to quantum anomalous Hall effect and axion insulator phase. MnBi₄Te₇ is a recently discovered antiferromagnetic topological insulator with T_N ∼ 12.5 K, which is composed of an alternatively stacked magnetic layer (MnBi₂Te₄) and nonmagnetic layer (Bi₂Te₃). By means of scanning tunneling spectroscopy, we clearly observe the electronic state present at a step edge of a magnetic MnBi₂Te₄ layer but absent at nonmagnetic Bi₂Te₃ layers at 4.5 K. Furthermore, we find that as the temperature rises above T_N the edge state vanishes, while the point defect induced state persists upon an increase in temperature. These results confirm the observation of magnetism-induced edge states. Our analysis based on an axion insulator theory reveals that the nontrivial topological nature of the observed edge state.

Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping

In this work, we investigate the topological phase transitions in an effective model for a topological thin film with high-frequency pumping. In particular, our results show that the circularly polarized light can break the time-reversal symmetry and induce the quantum anomalous Hall insulator (QAHI) phase. Meanwhile, the bulk magnetic moment can also break the time-reversal symmetry. Therefore, it shows rich phase diagram by tuning the intensity of the light and the thickness of the thin film. Using the parameters fitted by experimental data, we give the topological phase diagram of the Cr-doped Bi₂Se₃thin film, showing that by modulating the strength of the polarized optical field in an experimentally accessible range, there are four different phases: the normal insulator phase, the time-reversal-symmetry-broken quantum spin Hall insulator phase, and two different QAHI phases with opposite Chern numbers. Comparing with the non-doped Bi₂Se₃, it is found that the interplay between the light and bulk magnetic moment separates the two different QAHI phases with opposite Chern numbers. The results show that an intrinsic magnetic topological insulator with high-frequency pumping is an ideal platform for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

Thickness-Driven Quantum Anomalous Hall Phase Transition in Magnetic Topological Insulator Thin Films

The quantized version of the anomalous Hall effect realized in magnetic topological insulators (MTIs) has great potential for the development of topological quantum physics and low-power electronic/spintronic applications. Here we report the thickness-tailored quantum anomalous Hall (QAH) effect in Cr-doped (Bi,Sb)₂Te₃ thin films by tuning the system across the two-dimensional (2D) limit. In addition to the Chern number-related QAH phase transition, we also demonstrate that the induced hybridization gap plays an indispensable role in determining the ground magnetic state of the MTIs; namely, the spontaneous magnetization owing to considerable Van Vleck spin susceptibility guarantees the zero-field QAH state with unitary scaling law in thick samples, while the quantization of the Hall conductance can only be achieved with the assistance of external magnetic fields in ultrathin films. The modulation of topology and magnetism through structural engineering may provide useful guidance for the pursuit of other QAH-based phase diagrams and functionalities.

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.

Charge transport in magnetic topological ultra-thin films: the effect of structural inversion asymmetry

We study the effect of structural inversion asymmetry, induced by the presence of substrates or by external electric fields, on charge transport in magnetic topological ultra-thin films. We consider general orientations of the magnetic impurities. Our results are based on the Boltzmann formalism along with a modified relaxation time scheme. We show that the structural inversion asymmetry enhances the charge transport anisotropy induced by the magnetic impurities and when only one conduction subband contributes to the charge transport a dissipationless charge current is accessible. We demonstrate how a substrate or gate voltage can control the effect of the magnetic impurities on the charge transport, and how this depends on the orientation of the magnetic impurities.

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

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

Critical Behavior and Universal Signature of an Axion Insulator State

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

A non-volatile cryogenic random-access memory based on the quantum anomalous Hall effect

The interplay between ferromagnetism and topological properties of electronic band structures leads to a precise quantization of Hall resistance without any external magnetic field. This so-called quantum anomalous Hall effect (QAHE) is born out of topological correlations, and is oblivious of low-sample quality. It was envisioned to lead towards dissipation-less and topologically protected electronics. However, no clear framework of how to design such an electronic device out of it exists. Here we construct an ultra-low power, non-volatile, cryogenic memory architecture leveraging the QAHE phenomenon. Our design promises orders of magnitude lower cell area compared with the state-of-the-art cryogenic memory technologies. We harness the fundamentally quantized Hall resistance levels in moiré graphene heterostructures to store non-volatile binary bits (1, 0). We perform the memory write operation through controlled hysteretic switching between the quantized Hall states, using nano-ampere level currents with opposite polarities. The non-destructive read operation is performed by sensing the polarity of the transverse Hall voltage using a separate pair of terminals. We custom design the memory architecture with a novel sensing mechanism to avoid accidental data corruption, ensure highest memory density and minimize array leakage power. Our design provides a pathway towards realizing topologically protected memory devices.

Fully spin-polarized Weyl fermions and in/out-of-plane quantum anomalous Hall effects in a two-dimensional d0 ferromagnet

The quantum anomalous Hall effect (QAHE) in intrinsic ferromagnets has attracted considerable attention recently. Previously, studies of the QAHE have mostly focused on the default assumption of out-of-plane magnetization. In fact, the QAHE can also be achieved via in-plane magnetization, but such candidate materials are very scarce. Here, we find that two-dimensional (2D) YN₂ not only possesses the previously reported out-of-plane QAHE, but it also possesses a tunable in-plane QAHE. More importantly, unlike the previously reported in-plane QAHE in d/f-type ferromagnets, here we report the effect in a 2D d⁰ ferromagnet, namely YN₂, for the first time. In the ground state, a YN₂ monolayer has a half-metal band structure, and manifests six pairs of fully spin-polarized Weyl points at the Fermi level. When spin-orbit coupling is included, the YN₂ monolayer can realize multiple topological phases, determined based on the magnetization direction. Under in-plane magnetization, the YN₂ monolayer shows either the Weyl state or in-plane QAHE state. Remarkably, the Chern number (±1) and the propagating direction of QAHE edge channels can be continuously switched via shifting the direction of the in-plane magnetic field. When magnetization is applied out-of-plane, the YN₂ monolayer realizes an out-of-plane QAHE phase with a high Chern number of 3. The nontrivial edge states for all the topological phases in the YN₂ monolayer have been clearly identified. This work suggests that 2D YN₂ is an excellent candidate for investigating in-plane QAHE phases in d⁰ ferromagnets.

Current-induced switching of proximity-induced ferromagnetic surface states in a topological insulator

Electrical manipulation of magnetization could be an essential function for energy-efficient spintronics technology. A magnetic topological insulator, possessing a magnetically gapped surface state with spin-polarized electrons, not only exhibits exotic topological phases relevant to the quantum anomalous Hall state but also enables the electrical control of its magnetic state at the surface. Here, we demonstrate efficient current-induced switching of the surface ferromagnetism in hetero-bilayers consisting of the topological insulator (Bi_1-xSb_x)₂Te₃ and the ferromagnetic insulator Cr₂Ge₂Te₆, where the proximity-induced ferromagnetic surface states play two roles: efficient charge-to-spin current conversion and emergence of large anomalous Hall effect. The sign reversal of the surface ferromagnetic states with current injection is clearly observed, accompanying the nearly full magnetization reversal in the adjacent insulating Cr₂Ge₂Te₆ layer of an optimal thickness range. The present results may facilitate an electrical control of dissipationless topological-current circuits.

Electrical manipulation of magnetization in devices made of topological materials may be an essential route towards future spintronics technology. Here, Mogi et al. show efficient current-induced switching of surface ferromagnetism in hetero-bilayers of topological insulator (Bi_1-xSb_x)₂Te₃ and ferromagnetic insulator Cr₂Ge₂Te₆.

Large non-reciprocal charge transport mediated by quantum anomalous Hall edge states

The topological nature of the quantum anomalous Hall effect (QAHE) causes a dissipationless chiral edge current at the sample boundary^1,2. Of fundamental interest is whether the chirality of the band structure manifests itself in charge transport properties. Here we report the observation of large non-reciprocal charge transport³ in a magnetic topological insulator, Cr-doped (Bi,Sb)₂Te₃. When the surface massive Dirac band is slightly carrier doped by a gate voltage, the edge state starts to dissipate and exhibits a current-direction-dependent resistance with a directional difference as large as 26%. The polarity of this diode effect depends on the magnetization direction as well as on the carrier type, electrons or holes. The correlation between the non-reciprocal resistance and the Hall resistance indicates that the non-reciprocity originates from the interplay between the chiral edge state and the Dirac surface state.

Termination switching of antiferromagnetic proximity effect in topological insulator

This work reports the ferromagnetism of topological insulator, (Bi,Sb)2Te3 (BST), with a Curie temperature of approximately 120 K induced by magnetic proximity effect (MPE) of an antiferromagnetic CrSe. The MPE was shown to be highly dependent on the stacking order of the heterostructure, as well as the interface symmetry: Growing CrSe on top of BST results in induced ferromagnetism, while growing BST on CrSe yielded no evidence of an MPE. Cr-termination in the former case leads to double-exchange interactions between Cr3+ surface states and Cr2+ bulk states. This Cr3+-Cr2+ exchange stabilizes the ferromagnetic order localized at the interface and magnetically polarizes the BST Sb band. In contrast, Se-termination at the CrSe/BST interface yields no detectable MPE. These results directly confirm the MPE in BST films and provide critical insights into the sensitivity of the surface state.

Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr₂ O₃ . The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂ O₃ and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.

Robust A-Type Order and Spin-Flop Transition on the Surface of the Antiferromagnetic Topological Insulator MnBi_{2}Te_{4}

Here, we present microscopic evidence of the persistence of uniaxial A-type antiferromagnetic order to the surface layers of MnBi_{2}Te_{4} single crystals using magnetic force microscopy. Our results reveal termination-dependent magnetic contrast across both surface step edges and domain walls, which can be screened by thin layers of soft magnetism. The robust surface A-type order is further corroborated by the observation of termination-dependent surface spin-flop transitions, which have been theoretically proposed decades ago. Our results not only provide key ingredients for understanding the electronic properties of the antiferromagnetic topological insulator MnBi_{2}Te_{4}, but also open a new paradigm for exploring intrinsic surface metamagnetic transitions in natural antiferromagnets.

Probing the low-temperature limit of the quantum anomalous Hall effect

Quantum anomalous Hall effect has been observed in magnetically doped topological insulators. However, full quantization, up until now, is limited within the sub-1 K temperature regime, although the material's magnetic ordering temperature can go beyond 100 K. Here, we study the temperature limiting factors of the effect in Cr-doped (BiSb)2Te3 systems using both transport and magneto-optical methods. By deliberate control of the thin-film thickness and doping profile, we revealed that the low occurring temperature of quantum anomalous Hall effect in current material system is a combined result of weak ferromagnetism and trivial band involvement. Our findings may provide important insights into the search for high-temperature quantum anomalous Hall insulator and other topologically related phenomena.

Magnetic Imaging of Domain Walls in the Antiferromagnetic Topological Insulator MnBi2Te4

The control of domain walls or spin textures is crucial for spintronic applications of antiferromagnets. Despite many efforts, it has been challenging to directly visualize antiferromagnetic domains or domain walls with nanoscale resolution, especially in magnetic field. Here, we report magnetic imaging of domain walls in several uniaxial antiferromagnets, the topological insulator MnBi₂Te₄ family, using cryogenic magnetic force microscopy (MFM). Our MFM results reveal higher magnetic susceptibility inside the domain walls than in domains. Domain walls in these antiferromagnets form randomly with strong thermal and magnetic field dependence. The direct visualization of these domain walls and domain structures in the magnetic field will not only facilitate the exploration of intrinsic topological phenomena in antiferromagnetic topological insulators but will also open a new path toward control and manipulation of domain walls or spin textures in functional antiferromagnets.

Spectroscopic fingerprint of chiral Majorana modes at the edge of a quantum anomalous Hall insulator/superconductor heterostructure

With the recent discovery of the quantum anomalous Hall insulator (QAHI), which exhibits the conductive quantum Hall edge states without external magnetic field, it becomes possible to create a topological superconductor (SC) by introducing superconductivity into these edge states. In this case, 2 distinct topological superconducting phases with 1 or 2 chiral Majorana edge modes were theoretically predicted, characterized by Chern numbers (N) of 1 and 2, respectively. We present spectroscopic evidence from Andreev reflection experiments for the presence of chiral Majorana modes in an Nb/(Cr_0.12Bi_0.26Sb_0.62)₂Te₃ heterostructure with distinct signatures attributed to 2 different topological superconducting phases. The results are in qualitatively good agreement with the theoretical predictions.

Intrinsic quantized anomalous Hall effect in a moiré heterostructure

The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.

Quantum-Hall to Insulator Transition in Ultra-Low-Carrier-Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron-hole puddles smearing its energy landscape. Here, by developing ultra-low-carrier density topological insulator Sb₂ Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum-Hall-to-insulator-transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum-Hall-to-insulator-transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.

Effects of Random Domains on the Zero Hall Plateau in the Quantum Anomalous Hall Effect

Recently, a zero Hall conductance plateau with random domains was experimentally observed in the quantum anomalous Hall (QAH) effect. We study the effects of random domains on the zero Hall plateau in QAH insulators. We find that the structure inversion symmetry determines the scaling property of the zero Hall plateau transition in the QAH systems. In the presence of structure inversion symmetry, the zero Hall plateau state shows a quantum-Hall-type critical point, originating from the two decoupled subsystems with opposite Chern numbers. However, the absence of structure inversion symmetry leads to a mixture between these two subsystems, gives rise to a line of critical points, and dramatically changes the scaling behavior. Hereinto, we predict a Berezinskii-Kosterlitz-Thouless-type transition during the Hall conductance plateau switching in the QAH insulators. Our results are instructive for both theoretic understanding of the zero Hall plateau transition and future transport experiments in the QAH insulators.

Multiple Chiral Majorana Fermion Modes and Quantum Transport

The chiral Majorana fermion is a massless self-conjugate fermionic particle that could arise as the quasiparticle edge state of a two-dimensonal topological state of matter. Here we propose a new platform for a chiral topological superconductor (TSC) in two dimensions with multiple N chiral Majorana fermions from a quantized anomalous Hall insulator in proximity to an s-wave superconductor with nontrivial band topology. A concrete example is that a N=3 chiral TSC is realized by coupling a magnetic topological insulator to the ion-based superconductor such as FeTe_{0.55}Se_{0.45}. We further propose the electrical and thermal transport experiments to detect the Majorana nature of three chiral edge fermions. A smoking gun signature is that the two-terminal electrical conductance of a quantized anomalous Hall-TSC junction obeys a unique distribution averaged to (2/3)e^{2}/h, which is due to the random edge mode mixing of chiral Majorana fermions and is distinguished from possible trivial explanations. The homogenous system proposed here provides an ideal platform for studying the exotic physics of chiral Majorana fermions.

Exchange-biasing topological charges by antiferromagnetism

Geometric Hall effect is induced by the emergent gauge field experienced by the carriers adiabatically passing through certain real-space topological spin textures, which is a probe to non-trivial spin textures, such as magnetic skyrmions. We report experimental indications of spin-texture topological charges induced in heterostructures of a topological insulator (Bi,Sb)2Te3 coupled to an antiferromagnet MnTe. Through a seeding effect, the pinned spins at the interface leads to a tunable modification of the averaged real-space topological charge. This effect experimentally manifests as a modification of the field-dependent geometric Hall effect when the system is field-cooled along different directions. This heterostructure represents a platform for manipulating magnetic topological transitions using antiferromagnetic order.

Proximity-induced magnetism and an anomalous Hall effect in Bi2Se3/LaCoO3: a topological insulator/ferromagnetic insulator thin film heterostructure

Inducing magnetism in a topological insulator (TI) by exchange coupling with a ferromagnetic insulator (FMI) will break the time-reversal symmetry of topological surface states, offering possibilities to realize several predicted novel magneto-electric effects. Seeking suitable FMI materials is crucial for the coupling of heterojunctions, and yet is challenging as well and only a few kinds have been explored. In this report, we introduce epitaxial LaCoO3 thin films on a SrTiO3 substrate, which is an insulating ferromagnet with a Curie temperature of TC ∼ 85 K, to be combined with TIs for proximity coupling. Thin films of the prototype topological insulator, Bi2Se3, are successfully grown onto the (001) surface of LaCoO3/SrTiO3, forming a high-quality TI/FMI heterostructure with a sharp interface. The magnetic and transport measurements manifest the emergence of a ferromagnetic phase in Bi2Se3 films, with additional induced moments and a suppressed weak antilocalization effect, while preserving the carrier mobility of the intrinsic Bi2Se3 films at the same time. Moreover, a signal of an anomalous Hall effect is observed and persists up to temperatures above 100 K, paving the way towards spintronic device applications.

Quantized chiral edge conduction on domain walls of a magnetic topological insulator

Electronic ordering in magnetic and dielectric materials forms domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables nonvolatile responses against minute external fields. Here, we realize chiral edge states (CESs) on the magnetic DWs of a magnetic topological insulator. We design and fabricate the magnetic domains in the quantum anomalous Hall state with the tip of a magnetic force microscope and prove the existence of the chiral one-dimensional edge conduction along the prescribed DWs through transport measurements. The proof-of-concept devices based on reconfigurable CESs and Landauer-Büttiker formalism are realized for multiple-domain configurations with well-defined DW channels. Our results may lead to the realization of low-power-consumption spintronic devices.

Realization of the Axion Insulator State in Quantum Anomalous Hall Sandwich Heterostructures

The "magnetoelectric effect" arises from the coupling between magnetic and electric properties in materials. The Z_{2} invariant of topological insulators (TIs) leads to a quantized version of this phenomenon, known as the topological magnetoelectric (TME) effect. This effect can be realized in a new topological phase called an "axion insulator" whose surface states are all gapped but the interior still obeys time reversal symmetry. We demonstrate such a phase using electrical transport measurements in a quantum anomalous Hall (QAH) sandwich heterostructure, in which two compositionally different magnetic TI layers are separated by an undoped TI layer. Magnetic force microscopy images of the same sample reveal sequential magnetization reversals of the top and bottom layers at different coercive fields, a consequence of the weak interlayer exchange coupling due to the spacer. When the magnetization is antiparallel, both the Hall resistance and Hall conductance show zero plateaus, accompanied by a large longitudinal resistance and vanishing longitudinal conductance, indicating the realization of an axion insulator state. Our findings thus show evidence for a phase of matter distinct from the established QAH state and provide a promising platform for the realization of the TME effect.

Zero-field edge plasmons in a magnetic topological insulator

Incorporating ferromagnetic dopants into three-dimensional topological insulator thin films has recently led to the realisation of the quantum anomalous Hall effect. These materials are of great interest since they may support electrical currents that flow without resistance, even at zero magnetic field. To date, the quantum anomalous Hall effect has been investigated using low-frequency transport measurements. However, transport results can be difficult to interpret due to the presence of parallel conductive paths, or because additional non-chiral edge channels may exist. Here we move beyond transport measurements by probing the microwave response of a magnetised disk of Cr-(Bi,Sb)₂Te₃. We identify features associated with chiral edge plasmons, a signature that robust edge channels are intrinsic to this material system. Our results provide a measure of the velocity of edge excitations without contacting the sample, and pave the way for an on-chip circuit element of practical importance: the zero-field microwave circulator.

Direct measurement of edge transport in the quantum anomalous Hall effect can be made difficult due to the presence of parallel conductive paths. Here, Mahoney et al. report features associated with chiral edge plasmons, a signature of robust edge states, by probing the zero-field microwave response of a magnetised disk of Cr-(Bi,Sb)₂Te₃.

Topological states of condensed matter

Topological states of quantum matter have been investigated intensively in recent years in materials science and condensed matter physics. The field developed explosively largely because of the precise theoretical predictions, well-controlled materials processing, and novel characterization techniques. In this Perspective, we review recent progress in topological insulators, the quantum anomalous Hall effect, chiral topological superconductors, helical topological superconductors and Weyl semimetals.

Structural properties of thin-film ferromagnetic topological insulators

We present a comprehensive study of the crystal structure of the thin-film, ferromagnetic topological insulator (Bi, Sb)_2−xV_xTe₃. The dissipationless quantum anomalous Hall edge states it manifests are of particular interest for spintronics, as a natural spin filter or pure spin source, and as qubits for topological quantum computing. For ranges typically used in experiments, we investigate the effect of doping, substrate choice and film thickness on the (Bi, Sb)₂Te₃ unit cell using high-resolution X-ray diffractometry. Scanning transmission electron microscopy and energy-dispersive X-ray spectroscopy measurements provide local structural and interfacial information. We find that the unit cell is unaffected in-plane by vanadium doping changes, and remains unchanged over a thickness range of 4–10 quintuple layers (1 QL ≈ 1 nm). The in-plane lattice parameter (a) also remains the same in films grown on different substrate materials. However, out-of-plane the c-axis increases with the doping level and thicknesses >10 QL, and is potentially reduced in films grown on Si (1 1 1).

RETRACTED: Chiral Majorana fermion modes in a quantum anomalous Hall insulator-superconductor structure

Majorana fermion is a hypothetical particle that is its own antiparticle. We report transport measurements that suggest the existence of one-dimensional chiral Majorana fermion modes in the hybrid system of a quantum anomalous Hall insulator thin film coupled with a superconductor. As the external magnetic field is swept, half-integer quantized conductance plateaus are observed at the locations of magnetization reversals, giving a distinct signature of the Majorana fermion modes. This transport signature is reproducible over many magnetic field sweeps and appears at different temperatures. This finding may open up an avenue to control Majorana fermions for implementing robust topological quantum computing.

Weak Localization and Antilocalization in Topological Materials with Impurity Spin-Orbit Interactions

Topological materials have attracted considerable experimental and theoretical attention. They exhibit strong spin-orbit coupling both in the band structure (intrinsic) and in the impurity potentials (extrinsic), although the latter is often neglected. In this work, we discuss weak localization and antilocalization of massless Dirac fermions in topological insulators and massive Dirac fermions in Weyl semimetal thin films, taking into account both intrinsic and extrinsic spin-orbit interactions. The physics is governed by the complex interplay of the chiral spin texture, quasiparticle mass, and scalar and spin-orbit scattering. We demonstrate that terms linear in the extrinsic spin-orbit scattering are generally present in the Bloch and momentum relaxation times in all topological materials, and the correction to the diffusion constant is linear in the strength of the extrinsic spin-orbit. In topological insulators, which have zero quasiparticle mass, the terms linear in the impurity spin-orbit coupling lead to an observable density dependence in the weak antilocalization correction. They produce substantial qualitative modifications to the magnetoconductivity, differing greatly from the conventional Hikami-Larkin-Nagaoka formula traditionally used in experimental fits, which predicts a crossover from weak localization to antilocalization as a function of the extrinsic spin-orbit strength. In contrast, our analysis reveals that topological insulators always exhibit weak antilocalization. In Weyl semimetal thin films having intermediate to large values of the quasiparticle mass, we show that extrinsic spin-orbit scattering strongly affects the boundary of the weak localization to antilocalization transition. We produce a complete phase diagram for this transition as a function of the mass and spin-orbit scattering strength. Throughout the paper, we discuss implications for experimental work, and, at the end, we provide a brief comparison with transition metal dichalcogenides.

Scaling of the Quantum Anomalous Hall Effect as an Indicator of Axion Electrodynamics

We report on the scaling behavior of V-doped (Bi,Sb)_{2}Te_{3} samples in the quantum anomalous Hall regime for samples of various thickness. While previous quantum anomalous Hall measurements showed the same scaling as expected from a two-dimensional integer quantum Hall state, we observe a dimensional crossover to three spatial dimensions as a function of layer thickness. In the limit of a sufficiently thick layer, we find scaling behavior matching the flow diagram of two parallel conducting topological surface states of a three-dimensional topological insulator each featuring a fractional shift of 1/2e^{2}/h in the flow diagram Hall conductivity, while we recover the expected integer quantum Hall behavior for thinner layers. This constitutes the observation of a distinct type of quantum anomalous Hall effect, resulting from 1/2e^{2}/h Hall conductance quantization of three-dimensional topological insulator surface states, in an experiment which does not require decomposition of the signal to separate the contribution of two surfaces. This provides a possible experimental link between quantum Hall physics and axion electrodynamics.

Above 400-K robust perpendicular ferromagnetic phase in a topological insulator

The quantum anomalous Hall effect (QAHE) that emerges under broken time-reversal symmetry in topological insulators (TIs) exhibits many fascinating physical properties for potential applications in nanoelectronics and spintronics. However, in transition metal-doped TIs, the only experimentally demonstrated QAHE system to date, the QAHE is lost at practically relevant temperatures. This constraint is imposed by the relatively low Curie temperature (T_c) and inherent spin disorder associated with the random magnetic dopants. We demonstrate drastically enhanced T_c by exchange coupling TIs to Tm₃Fe₅O₁₂, a high-T_c magnetic insulator with perpendicular magnetic anisotropy. Signatures showing that the TI surface states acquire robust ferromagnetism are revealed by distinct squared anomalous Hall hysteresis loops at 400 K. Point-contact Andreev reflection spectroscopy confirms that the TI surface is spin-polarized. The greatly enhanced T_c, absence of spin disorder, and perpendicular anisotropy are all essential to the occurrence of the QAHE at high temperatures.

A magnetic heterostructure of topological insulators as a candidate for an axion insulator

The axion insulator which may exhibit an exotic quantized magnetoelectric effect is one of the most interesting quantum phases predicted for the three-dimensional topological insulator (TI). The axion insulator state is expected to show up in magnetically doped TIs with magnetizations pointing inwards and outwards from the respective surfaces. Towards the realization of the axion insulator, we here engineered a TI heterostructure in which magnetic ions (Cr) are modulation-doped only in the vicinity of the top and bottom surfaces of the TI ((Bi,Sb)₂Te₃) film. A separation layer between the two magnetic layers weakens interlayer coupling between them, enabling the magnetization reversal of individual layers. We demonstrate the realization of the axion insulator by observing a zero Hall plateau (ZHP) (where both the Hall and longitudinal conductivity become zero) in the electric transport properties, excluding the other possible origins for the ZHP. The manifestation of the axion insulator can lead to a new stage of research on novel magnetoelectric responses in topological matter.