High-temperature Quantum Anomalous Hall Research Articles

Experimental observation of gapped topological surface states in Sb-doped MnBi4Te7

The realization of intrinsic magnetic topological insulators offers an ideal platform to investigate high-temperature quantum anomalous Hall effect as well as quantum devices. The family of MnBi2Te4(Bi2Te3)n has been confirmed that it belongs to this system. However, whether there is a bandgap in the surface states remains controversial. In this work, the ferromagnetism in Sb-doped MnBi4Te7 is confirmed by magnetic transport. Utilizing angle-resolved photoemission spectroscopy, we demonstrate the nontrivial topology in Mn(Bi0.7Sb0.3)4Te7 with an energy gap on the MnBi2Te4 termination. As well, we detect distinct topological surface states on two different terminations. Our results provide spectral evidence of an energy gap in the topological surface states.

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.

Signature of spin-phonon coupling driven charge density wave in a kagome magnet

The intertwining between spin, charge, and lattice degrees of freedom can give rise to unusual macroscopic quantum states, including high-temperature superconductivity and quantum anomalous Hall effects. Recently, a charge density wave (CDW) has been observed in the kagome antiferromagnet FeGe, indicative of possible intertwining physics. An outstanding question is that whether magnetic correlation is fundamental for the spontaneous spatial symmetry breaking orders. Here, utilizing elastic and high-resolution inelastic x-ray scattering, we observe a c-axis superlattice vector that coexists with the 2times2times1 CDW vectors in the kagome plane. Most interestingly, between the magnetic and CDW transition temperatures, the phonon dynamical structure factor shows a giant phonon-energy hardening and a substantial phonon linewidth broadening near the c-axis wavevectors, both signaling the spin-phonon coupling. By first principles and model calculations, we show that both the static spin polarization and dynamic spin excitations intertwine with the phonon to drive the spatial symmetry breaking in FeGe.

Bi2Te3-intercalated MnBi2Te4: ideal candidate to explore intrinsic Chern insulator and high-temperature quantum anomalous Hall effect

The recently discovered magnetic topological insulator of MnBi2Te4 (MBT), has been demonstrated to realize the quantum anomalous Hall (QAH) effect, while the naturally antiferromagnetic (AFM) interlayer coupling in MBT results in that the QAH effect can only be realized in odd-layered systems and at low temperature. Using first-principles calculations, we find that intercalating Bi2Te3 (BT) layers into MBT by forming MBT/(BT) n /MBT (n = 1–6) heterostructures can induce magnetic phase transition from AFM to ferromagnetic (FM) interlayer coupling when n⩾ 3. Specifically, MBT/(BT)3/MBT and MBT/(BT)4/MBT respectively host Curie temperatures T c of 14 K and 11 K, which fits well the experimentally measured T c of 12 K. Detailed band structure calculations and topological identification show that the QAH phases are well preserved for all FM heterostructures. And the topological mechanism of MBT/(BT) n /MBT as a function of n is revealed by employing continuum model analysis. Most importantly, the FM MBT/(BT)4/MBT has already been experimentally fabricated. Thus, our work provides a practical guideline to explore high-temperature QAH effect in MBT family of 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.

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.

Gate-Tunable Proximity Effects in Graphene on Layered Magnetic Insulators.

The extreme versatility of van der Waals materials originates from their ability to exhibit new electronic properties when assembled in close proximity to dissimilar crystals. For example, although graphene is inherently nonmagnetic, recent work has reported a magnetic proximity effect in graphene interfaced with magnetic substrates, potentially enabling a pathway toward achieving a high-temperature quantum anomalous Hall effect. Here, we investigate heterostructures of graphene and chromium trihalide magnetic insulators (CrI3, CrBr3, and CrCl3). Surprisingly, we are unable to detect a magnetic exchange field in the graphene but instead discover proximity effects featuring unprecedented gate tunability. The graphene becomes highly hole-doped due to charge transfer from the neighboring magnetic insulator and further exhibits a variety of atypical gate-dependent transport features. The charge transfer can additionally be altered upon switching the magnetic states of the nearest CrI3 layers. Our results provide a roadmap for exploiting proximity effects arising in graphene coupled to magnetic insulators.

Strain-engineered topological phase transitions in ferrovalley 2H−RuCl2 monolayer

Ferrovalley and topology are two basic concepts in both fundamental research fields and emerging device applications. So far, reports are extremely scarce regarding the coupling of these two scenarios in a single material system. By first-principles calculations and Monte Carlo simulations, we predict a highly stable intrinsic ferrovalley $2H\text{\ensuremath{-}}{\mathrm{RuCl}}_{\text{2}}$ semiconductor with an easy out-of-plane magnetization and a high Curie temperature of 260 K. Due to the combination of exchange interaction and spin-orbit coupling, the system exhibits a spontaneous valley polarization of 240 meV in the top valence band, which is further confirmed by a first-order perturbation theory. Moreover, its out-of-plane ferromagnetic ordering can remain rather robust and survive up to 547 K under $\ensuremath{-}5$% compressive strain well above room temperature. On the other hand, the application of tensile strain can drive the system from the ferrovalley phase into a half-valley-metal state with 100% spin and valley polarizations, followed then by a quantum anomalous Hall (QAH) phase in support of scarce high-temperature QAH effect. Beyond around 2% tensile strain, the system is switched to the in-plane magnetization. If the magnetization is steered to the out-of-plane direction through overcoming the magnetic anisotropy energy barriers, the system is further transitioned from the QAH phase to another half-valley-metal state with the rise of tensile strain, and finally restores to the initial ferrovalley phase. Once synthesized, monolayer $2H\text{\ensuremath{-}}{\mathrm{RuCl}}_{\text{2}}$ would find many important applications in spintronic, valleytronic, and topological electronic nanodevices.

Designing light-element materials with large effective spin-orbit coupling

Spin-orbit coupling (SOC), which is the core of many condensed-matter phenomena such as nontrivial band gap and magnetocrystalline anisotropy, is generally considered appreciable only in heavy elements. This is detrimental to the synthesis and application of functional materials. Therefore, amplifying the SOC effect in light elements is crucial. Herein, focusing on 3d and 4d systems, we demonstrate that the interplay between crystal symmetry and electron correlation can significantly enhance the SOC effect in certain partially occupied orbital multiplets through the self-consistently reinforced orbital polarization as a pivot. Thereafter, we provide design principles and comprehensive databases, where we list all the Wyckoff positions and site symmetries in all two-dimensional (2D) and three-dimensional crystals that could have enhanced SOC effect. Additionally, we predict nine material candidates from our selected 2D material pool as high-temperature quantum anomalous Hall insulators with large nontrivial band gaps of hundreds of meV. Our study provides an efficient and straightforward way for predicting promising SOC-active materials, relieving the use of heavy elements for next-generation spin-orbitronic materials and devices.

Photoinduced quantum anomalous Hall states in the topological Anderson insulator

The realization of the quantum anomalous Hall (QAH) effect without magnetic doping attracts intensive interest since magnetically doped topological insulators usually possess inhomogeneity of ferromagnetic order. Here, we propose a different strategy to realize intriguing QAH states arising from the interplay of light and non-magnetic disorder in two-dimensional topologically trivial systems. By combining the Born approximation and Floquet theory, we show that a time-reversal invariant disorder-induced topological insulator, known as the topological Anderson insulator (TAI), would evolve into a time-reversal broken TAI and then into a QAH insulator by shining circularly polarized light. We utilize spin and charge Hall conductivities, which can be measured in experiments directly, to distinguish these three different topological phases. This work not only offers an exciting opportunity to realize the high-temperature QAH effect without magnetic orders, but also is important for applications of topological states to spintronics.

A generic dual d-band model for interlayer ferromagnetic coupling in a transition-metal doped MnBi2Te4 family of materials

Realization of ferromagnetic (FM) interlayer coupling in magnetic topological insulators (TIs) of the MnBi2Te4 family of materials (MBTs) may pave the way for realizing the high-temperature quantum anomalous Hall effect (high-T QAHE). Here we propose a generic dual d-band (DDB) model to elucidate the energy difference (ΔE = EAFM - EFM) between the AFM and FM coupling in transition-metal (TM)-doped MBTs, where the valence of TMs splits into d-t2g and d-eg sub-bands. Remarkably, the DDB shows that ΔE is universally determined by the relative position of the dopant (X) and Mn d-eg/t2g bands, . If ΔEd > 0, then ΔE > 0 and the desired FM coupling is favored. This surprisingly simple rule is confirmed by first-principles calculations of hole-type 3d and 4d TM dopants. Significantly, by applying the DDB model, we predict the high-T QAHE in the V-doped Mn2Bi2Te5, where the Curie temperature is enhanced by doubling of the MnTe layer, while the topological order mitigated by doping can be restored by strain.

Coexistence of ferromagnetism and topology by charge carrier engineering in the intrinsic magnetic topological insulator MnBi4Te7

Intrinsic magnetic topological insulators (MTIs) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ and $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ are expected to realize the high-temperature quantum anomalous Hall effect and dissipationless electrical transport. However, there is still a lack of ideal MTI candidates with magnetic ordering of the ferromagnetic (FM) ground state. Here, we show a MTI sample of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ which holds the coexistence of a FM behavior state and topological nontriviality. The dramatic modulation of the magnetism is induced by a charge carrier engineering process via the Sb substitution in the $\mathrm{Mn}{\mathrm{Bi}}_{4}{\mathrm{Te}}_{7}$ matrix with antiferromagnetic ordering. The evolution of magnetism in $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$ is systematically investigated by our magnetic measurements and theoretical calculations. The clear topological surface states of the FM sample of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ are further verified by angle-resolved photoemission spectroscopy. The demonstration of the intrinsic FM-MTI of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ in this paper sheds light on further material optimization of intrinsic MTIs and paves the way for further studies to clarify the relationships between topology, magnetism, and charge carriers in topological materials.

Evidence for one-dimensional chiral edge states in a magnetic Weyl semimetal Co3Sn2S2

The physical realization of Chern insulators is of fundamental and practical interest, as they are predicted to host the quantum anomalous Hall (QAH) effect and topologically protected chiral edge states which can carry dissipationless current. Current realizations of the QAH state often require complex heterostructures and sub-Kelvin temperatures, making the discovery of intrinsic, high temperature QAH systems of significant interest. In this work we show that time-reversal symmetry breaking Weyl semimetals, being essentially stacks of Chern insulators with inter-layer coupling, may provide a new platform for the higher temperature realization of robust chiral edge states. We present combined scanning tunneling spectroscopy and theoretical investigations of the magnetic Weyl semimetal, Co3Sn2S2. Using modeling and numerical simulations we find that depending on the strength of the interlayer coupling, chiral edge states can be localized on partially exposed kagome planes on the surfaces of a Weyl semimetal. Correspondingly, our dI/dV maps on the kagome Co3Sn terraces show topological states confined to the edges which display linear dispersion. This work provides a new paradigm for realizing chiral edge modes and provides a pathway for the realization of higher temperature QAH effect in magnetic Weyl systems in the two-dimensional limit.

Interlayer ferromagnetism and high-temperature quantum anomalous Hall effect in p -doped MnBi2Te4 multilayers

The interlayer antiferromagnetic coupling hinders the observation of quantum anomalous Hall effect in magnetic topological insulator $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$. We demonstrate that interlayer ferromagnetism can be established by utilizing the $p$-doping method in $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ multilayers. In two septuple layers system, the interlayer ferromagnetic coupling appears by doping nonmagnetic elements (e.g., N, P, As, Na, Mg, K, and Ca), due to the redistribution of orbital occupations of Mn. We further find that Mg and Ca elements are the most suitable candidates because of their low formation energy. Although, the $p$-doped two septuple layers exhibit topologically trivial band structure, the increase of layer thickness to three (four) septuple layers with Ca (Mg) dopants leads to the formation of the quantum anomalous Hall effect. Our proposed $p$-doping strategy without introducing additional magnetic disorder not only makes $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ become an ideal platform to realize the high-temperature quantum anomalous Hall effect without external magnetic field, but also can compensate the electrons from the intrinsic $n$-type defects in $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$.

Quarter-filled Kane-Mele Hubbard model: Dirac half metals

Recent experimental success in the realization of two-dimensional (2D) magnetism has stimulated the search for new magnetic 2D materials with strong magnetic anisotropy and high Curie temperature. One promising subgroup of 2D magnetic systems are Dirac half-metals (DHM) which have gained a lot of interest recently, as they host a high-temperature quantum anomalous Hall effect (QAHE). This article discusses predictions for intrinsic DHMs and identifies them as realizations of the Kane-Mele Hubbard model at quarter filling. This proposed unification contributes to a firmer understanding of these materials and suggests pathways for the discovery of new DHM systems.

First-principles calculations of two-dimensionalmagnetic materials

Two-dimensional (2D) magnetic materials have attracted intensive research interest owing to their extraordinary electronic properties, abundant tunable functionalities and promising device applications. Early experiments attempted to extrinsically introduce magnetism into 2D nonmagnetic materials, for instance, by defect engineering or magnetic proximity. These extrinsic engineering strategies usually lead to weak magnetism and are difficult to control experimentally and thus unfavorable for applications. The discovery of intrinsic ferromagnetism in 2D insulators CrGeTe3 and CrI3 has stimulated great research effort in the field. Besides, different kinds of 2D magnetic materials have been synthesized recently, including itinerant ferromagnets Fe3GeTe2, VSe2 and MnSe x , antiferromagnets NiPS3 and FePS3, and intrinsic magnetic topological material MnBi2Te4. 2D magnetic materials can be used to construct van der Waals heterojunctions to realize novel physical phenomena such as multiferroics and quantum anomalous Hall effect, as well as to develop spintronic devices such as magnetic tunneling junctions and spin-field-effect transistors. On the other hand, first-principles calculations have been widely applied in the study of condensed matter physics and material science. Density functional theory (DFT) in the framework of Kohn-Sham scheme is one of the most popular methods for first-principles calculations. The critical issue of DFT is to use suitable exchange-correlation functional for achieving computational efficiency and accuracy simultaneously. Commonly used exchange-correlation functional, such as local density approximation and generalized gradient approximation, can successfully describe various properties of most compounds comprised of main group elements, such as atomic and electronic structures. However, these local or semi-local functional cannot provide an accurate description of localized or strongly correlated electronic states, including open-shell d and f orbitals. More advanced methods, such as the DFT+ U and hybrid functional methods, are generally desired to study 2D magnetic materials. In this review, we firstly introduced general theoretical background and computational methods on magnetism, including theory of magnetic exchange interactions and magnetic anisotropy. Magnetic exchange interactions determine magnetic orders, which are classified into local magnetic exchange and itinerant magnetic exchange according to electronic properties of the system. Magnetic anisotropy is contributed by shape anisotropy and magnetocrystalline anisotropy, which are originated from magnetic dipolar interaction and spin-orbit coupling, respectively. Then we presented theoretical progresses on the study of 2D magnetic materials, focusing on four representative material systems: (1) 2D magnetic insulators CrGeTe3 and CrI3; (2) 2D ferromagnetic metal Fe3GeTe2; (3) 2D intrinsic magnetic topological material MnBi2Te4; (4) 2D high-temperature quantum anomalous Hall insulator LiFeSe. Through these example studies, we systematically introduced fundamental mechanisms of exchange coupling and magnetic anisotropy, feasible ways to tune electronic and magnetic properties, as well as new physics introduced by the interplay of magnetism and topology. Finally we offered an outlook on future first-principles research of 2D magnetic materials.

High-Temperature Quantum Anomalous Hall Insulators in Lithium-Decorated Iron-Based Superconductor Materials.

Quantum anomalous Hall (QAH) insulator is the key material to study emergent topological quantum effects, but its ultralow working temperature limits experiments. Here, by first-principles calculations, we find a family of stable two-dimensional (2D) structures generated by lithium decoration of layered iron-based superconductor materials Fe X(X=S,Se,Te), and predict room-temperature ferromagnetic semiconductors together with large-gap high-Chern-number QAH insulators in the 2D materials. The extremely robust ferromagnetic order is induced by the electron injection from Li to Fe and stabilized by strong ferromagnetic kinetic exchange in the 2D Fe layer. While in the absence of spin-orbit coupling (SOC), the ferromagnetism polarizes the system into a half Dirac semimetal state protected by mirror symmetry, the SOC effect results in a spontaneous breaking of mirror symmetry and introduces a Dirac mass term, which creates QAH states with sizable gaps (several tens of meV) and multiple chiral edge modes. We also find a 3D QAH insulator phase featured by a macroscopic number of chiral conduction channels in bulk LiOH-LiFe X. The findings open new opportunities to realize novel QAH physics and applications at high temperatures.

High-temperature quantum anomalous Hall regime in a MnBi2Te4/Bi2Te3 superlattice

The quantum anomalous Hall effect is a fundamental transport response of a topologically non-trivial system in zero magnetic field. Its physical origin relies on the intrinsically inverted electronic band structure and ferromagnetism, and its most consequential manifestation is the dissipation-free flow of chiral charge currents at the edges that can potentially transform future quantum electronics. Here we report a previously unknown Berry-curvature-driven anomalous Hall regime ('Q-window') at above-Kelvin temperatures in the magnetic topological bulk crystals where through growth Mn ions self-organize into a period-ordered MnBi$_2$Te$_4$/Bi$_2$Te$_3$ superlattice. Robust ferromagnetism of the MnBi$_2$Te$_4$ monolayers opens a large surface gap, and anomalous Hall conductance reaches an $e^2/h$ quantization plateau when the Fermi level is tuned into this gap within a Q-window in which the anomalous Hall conductance from the bulk is to a high precision zero. The quantization in this new regime is not obstructed by the bulk conduction channels and thus should be present in a broad family of topological magnets.

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.

The mechanism exploration for zero-field ferromagnetism in intrinsic topological insulator MnBi2Te4 by Bi2Te3 intercalations

Recent research on intrinsic magnetic topological insulators (MTIs), MnBi2Te4, sheds new light on the observation of a long-expected high-temperature quantum anomalous Hall effect (QAHE). However, the strong interlayered anti-ferromagnetic (AFM) coupling hinders the practical applications without applying a magnetic field. Thus, how to adjust the magnetism of this compound under zero field is essential. Here, we theoretically and experimentally study the magnetic properties of two new promising intrinsic MTI candidates MnBi4Te7 and MnBi6Te10, formed by intercalating the Bi2Te3 layer into MnBi2Te4. The first-principles calculations reveal that the relative energy between ferromagnetic (FM) and AFM states is greatly reduced by Bi2Te3 intercalations. The calculated energy barriers for the spin flipping process also point out that the metastable FM state is more easily retained by intercalation. Meanwhile, we also experimentally carry out magnetic and transport measurements on these materials. By increasing Bi2Te3 intercalations, the AFM coupling becomes weaker, and an almost fully polarized FM state can be preserved in MnBi6Te10 at low temperatures, which are consistent with our calculations. We believe that the demonstration of the intrinsic MTI preserving zero-field FM state and the in-depth investigation for the mechanism behind pave the way for investigating the high-temperature QAHE and the related physics.