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.

Coexistence of Superconductivity and Antiferromagnetism in Topological Magnet MnBi2Te4 Films.

The interface of two materials can harbor unexpected emergent phenomena. One example is interface-induced superconductivity. In this work, we employ molecular beam epitaxy to grow a series of heterostructures formed by stacking together two nonsuperconducting antiferromagnetic materials, an intrinsic antiferromagnetic topological insulator MnBi2Te4 and an antiferromagnetic iron chalcogenide FeTe. Our electrical transport measurements reveal interface-induced superconductivity in these heterostructures. By performing scanning tunneling microscopy and spectroscopy measurements, we observe a proximity-induced superconducting gap on the top surface of the MnBi2Te4 layer, confirming the coexistence of superconductivity and antiferromagnetism in the MnBi2Te4 layer. Our findings will advance the fundamental inquiries into the topological superconducting phase in hybrid devices and provide a promising platform for the exploration of chiral Majorana physics in MnBi2Te4-based heterostructures.

High-entropy engineering of the crystal and electronic structures in a Dirac material.

Dirac and Weyl semimetals are a central topic of contemporary condensed matter physics, and the discovery of new compounds with Dirac/Weyl electronic states is crucial to the advancement of topological materials and quantum technologies. Here we show a widely applicable strategy that uses high configuration entropy to engineer relativistic electronic states. We take the AMnSb2 (A = Ba, Sr, Ca, Eu, and Yb) Dirac material family as an example and demonstrate that mixing of Ba, Sr, Ca, Eu and Yb at the A site generates the compound (Ba0.38Sr0.14Ca0.16Eu0.16Yb0.16)MnSb2 (denoted as A5MnSb2), giving access to a polar structure with a space group that is not present in any of the parent compounds. A5MnSb2 is an entropy-stabilized phase that preserves its linear band dispersion despite considerable lattice disorder. Although both A5MnSb2 and AMnSb2 have quasi-two-dimensional crystal structures, the two-dimensional Dirac states in the pristine AMnSb2 evolve into a highly anisotropic quasi-three-dimensional Dirac state triggered by local structure distortions in the high-entropy phase, which is revealed by Shubnikov-de Haas oscillations measurements.

Hidden non-collinear spin-order induced topological surface states.

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Néel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.

Interface-induced superconductivity in magnetic topological insulators.

The interface between two different materials can show unexpected quantum phenomena. In this study, we used molecular beam epitaxy to synthesize heterostructures formed by stacking together two magnetic materials, a ferromagnetic topological insulator (TI) and an antiferromagnetic iron chalcogenide (FeTe). We observed emergent interface-induced superconductivity in these heterostructures and demonstrated the co-occurrence of superconductivity, ferromagnetism, and topological band structure in the magnetic TI layer-the three essential ingredients of chiral topological superconductivity (TSC). The unusual coexistence of ferromagnetism and superconductivity is accompanied by a high upper critical magnetic field that exceeds the Pauli paramagnetic limit for conventional superconductors at low temperatures. These magnetic TI/FeTe heterostructures with robust superconductivity and atomically sharp interfaces provide an ideal wafer-scale platform for the exploration of chiral TSC and Majorana physics.

Electrically Controlled Anomalous Hall Effect and Orbital Magnetization in Topological Magnet MnBi_{2}Te_{4}.

We propose an intrinsic mechanism to understand the even-odd effect, namely, opposite signs of anomalous Hall resistance and different shapes of hysteresis loops for even and odd septuple layers (SLs), of MBE-grown MnBi_{2}Te_{4} thin films with electron doping. The nonzero hysteresis loops in the anomalous Hall effect and magnetic circular dichroism for even-SLs MnBi_{2}Te_{4} films originate from two different antiferromagnetic (AFM) configurations with different zeroth Landau level energies of surface states. The complex form of the anomalous Hall hysteresis loop can be understood from two magnetic transitions, a transition between two AFM states followed by a second transition to the ferromagnetic state. Our model also clarifies the relationship and distinction between axion parameter and magnetoelectric coefficient, and shows an even-odd oscillation behavior of magnetoelectric coefficients in MnBi_{2}Te_{4} films.

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.

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.

Dirac-fermion-assisted interfacial superconductivity in epitaxial topological-insulator/iron-chalcogenide heterostructures.

Over the last decade, the possibility of realizing topological superconductivity (TSC) has generated much excitement. TSC can be created in electronic systems where the topological and superconducting orders coexist, motivating the continued exploration of candidate material platforms to this end. Here, we use molecular beam epitaxy (MBE) to synthesize heterostructures that host emergent interfacial superconductivity when a non-superconducting antiferromagnet (FeTe) is interfaced with a topological insulator (TI) (Bi, Sb)2Te3. By performing in-vacuo angle-resolved photoemission spectroscopy (ARPES) and ex-situ electrical transport measurements, we find that the superconducting transition temperature and the upper critical magnetic field are suppressed when the chemical potential approaches the Dirac point. We provide evidence to show that the observed interfacial superconductivity and its chemical potential dependence is the result of the competition between the Ruderman-Kittel-Kasuya-Yosida-type ferromagnetic coupling mediated by Dirac surface states and antiferromagnetic exchange couplings that generate the bicollinear antiferromagnetic order in the FeTe layer.

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.

Observation of fractionally quantized anomalous Hall effect.

The integer quantum anomalous Hall (QAH) effect is a lattice analogue of the quantum Hall effect at zero magnetic field1-3. This phenomenon occurs in systems with topologically non-trivial bands and spontaneous time-reversal symmetry breaking. Discovery of its fractional counterpart in the presence of strong electron correlations, that is, the fractional QAH effect4-7, would open a new chapter in condensed matter physics. Here we report the direct observation of both integer and fractional QAH effects in electrical measurements on twisted bilayer MoTe2. At zero magnetic field, near filling factor ν = -1 (one hole per moiré unit cell), we see an integer QAH plateau in the Hall resistance Rxy quantized to h/e2 ± 0.1%, whereas the longitudinal resistance Rxx vanishes. Remarkably, at ν = -2/3 and -3/5, we see plateau features in Rxy at [Formula: see text] and [Formula: see text], respectively, whereas Rxx remains small. All features shift linearly versus applied magnetic field with slopes matching the corresponding Chern numbers -1, -2/3 and -3/5, precisely as expected for integer and fractional QAH states. Additionally, at zero magnetic field, Rxy is approximately 2h/e2 near half-filling (ν = -1/2) and varies linearly as ν is tuned. This behaviour resembles that of the composite Fermi liquid in the half-filled lowest Landau level of a two-dimensional electron gas at high magnetic field8-14. Direct observation of the fractional QAH and associated effects enables research in charge fractionalization and anyonic statistics at zero magnetic field.

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.

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.

Proximity-induced superconductivity in epitaxial topological insulator/graphene/gallium heterostructures.

The introduction of superconductivity to the Dirac surface states of a topological insulator leads to a topological superconductor, which may support topological quantum computing through Majorana zero modes1,2. The development of a scalable material platform is key to the realization of topological quantum computing3,4. Here we report on the growth and properties of high-quality (Bi,Sb)2Te3/graphene/gallium heterostructures. Our synthetic approach enables atomically sharp layers at both hetero-interfaces, which in turn promotes proximity-induced superconductivity that originates in the gallium film. A lithography-free, van der Waals tunnel junction is developed to perform transport tunnelling spectroscopy. We find a robust, proximity-induced superconducting gap formed in the Dirac surface states in 5-10 quintuple-layer (Bi,Sb)2Te3/graphene/gallium heterostructures. The presence of a single Abrikosov vortex, where the Majorana zero modes are expected to reside, manifests in discrete conductance changes. The present material platform opens up opportunities for understanding and harnessing the application potential of topological superconductivity.

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.

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 AlOx 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.

Topological current divider in a Chern insulator junction.

A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi2Te4. We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi2Te4 as an emerging platform for topological circuits design.

Crossover from Ising- to Rashba-type superconductivity in epitaxial Bi2Se3/monolayer NbSe2 heterostructures.

A topological insulator (TI) interfaced with an s-wave superconductor has been predicted to host topological superconductivity. Although the growth of epitaxial TI films on s-wave superconductors has been achieved by molecular-beam epitaxy, it remains an outstanding challenge for synthesizing atomically thin TI/superconductor heterostructures, which are critical for engineering the topological superconducting phase. Here we used molecular-beam epitaxy to grow Bi2Se3 films with a controlled thickness on monolayer NbSe2 and performed in situ angle-resolved photoemission spectroscopy and ex situ magnetotransport measurements on these heterostructures. We found that the emergence of Rashba-type bulk quantum-well bands and spin-non-degenerate surface states coincides with a marked suppression of the in-plane upper critical magnetic field of the superconductivity in Bi2Se3/monolayer NbSe2 heterostructures. This is a signature of a crossover from Ising- to Rashba-type superconducting pairings, induced by altering the Bi2Se3 film thickness. Our work opens a route for exploring a robust topological superconducting phase in TI/Ising superconductor heterostructures.

Zero Magnetic Field Plateau Phase Transition in Higher Chern Number Quantum Anomalous Hall Insulators.

The plateau-to-plateau transition in quantum Hall effect under high magnetic fields is a celebrated quantum phase transition between two topological states. It can be achieved by either sweeping the magnetic field or tuning the carrier density. The recent realization of the quantum anomalous Hall (QAH) insulators with tunable Chern numbers introduces the channel degree of freedom to the dissipation-free chiral edge transport and makes the study of the quantum phase transition between two topological states under zero magnetic field possible. Here, we synthesized the magnetic topological insulator (TI)/TI pentalayer heterostructures with different Cr doping concentrations in the middle magnetic TI layers using molecular beam epitaxy. By performing transport measurements, we found a potential plateau phase transition between C=1 and C=2 QAH states under zero magnetic field. In tuning the transition, the Hall resistance monotonically decreases from h/e^{2} to h/2e^{2}, concurrently, the longitudinal resistance exhibits a maximum at the critical point. Our results show that the ratio between the Hall resistance and the longitudinal resistance is greater than 1 at the critical point, which indicates that the original chiral edge channel from the C=1 QAH state coexists with the dissipative bulk conduction channels. Subsequently, these bulk conduction channels appear to self-organize and form the second chiral edge channel in completing the plateau phase transition. Our study will motivate further investigations of this novel Chern number change-induced quantum phase transition and advance the development of the QAH chiral edge current-based electronic and spintronic devices.