Coexistence of Quantum Hall and Quantum Anomalous Hall Phases in Disordered MnBi_{2}Te_{4}

Exchange-Driven Chern States in High-Mobility Intrinsic Magnetic Topological Insulators

The layer-dependent Chern number (C) in MnBi_{2}Te_{4} is characterized by the presence of a Weyl semimetal state in the ferromagnetic coupling. However, the influence of a key factor, namely, the exchange coupling, remains unexplored. This study focuses on characterizing the C=2 state in MnBi_{2}Te_{4}, which is classified as a higher C state resulting from the anomalous n=0 Landau levels (LLs). Our findings demonstrate that the exchange coupling parameter strongly influences the formation of this Chern state, leading to a competition between the C=1 and 2 states. Moreover, the emergence of odd-even LL sequences, resulting from the breaking of LL degeneracy, provides compelling evidence for the strong exchange coupling strength. These findings highlight the significance of the exchange coupling in understanding the behavior of Chern states and LLs in magnetic quantum systems.

Progress on the antiferromagnetic topological insulator MnBi2Te4

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

Distinct Magnetic Gaps between Antiferromagnetic and Ferromagnetic Orders Driven by Surface Defects in the Topological Magnet MnBi_{2}Te_{4}

Many experiments observed a metallic behavior at zero magnetic fields (antiferromagnetic phase, AFM) in MnBi_{2}Te_{4} thin film transport, which coincides with gapless surface states observed by angle-resolved photoemission spectroscopy, while it can become a Chern insulator at field larger than 6 T (ferromagnetic phase, FM). Thus, the zero-field surface magnetism was once speculated to be different from the bulk AFM phase. However, recent magnetic force microscopy refutes this assumption by detecting persistent AFM order on the surface. In this Letter, we propose a mechanism related to surface defects that can rationalize these contradicting observations in different experiments. We find that co-antisites (exchanging Mn and Bi atoms in the surface van der Waals layer) can strongly suppress the magnetic gap down to several meV in the AFM phase without violating the magnetic order but preserve the magnetic gap in the FM phase. The different gap sizes between AFM and FM phases are caused by the exchange interaction cancellation or collaboration of the top two van der Waals layers manifested by defect-induced surface charge redistribution among the top two van der Waals layers. This theory can be validated by the position- and field-dependent gap in future surface spectroscopy measurements. Our work suggests suppressing related defects in samples to realize the quantum anomalous Hall insulator or axion insulator at zero fields.

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.

Graphene and Beyond: Recent Advances in Two-Dimensional Materials Synthesis, Properties, and Devices

Since the isolation of graphene in 2004, two-dimensional (2D) materials research has rapidly evolved into an entire subdiscipline in the physical sciences with a wide range of emergent applications. The unique 2D structure offers an open canvas to tailor and functionalize 2D materials through layer number, defects, morphology, moiré pattern, strain, and other control knobs. Through this review, we aim to highlight the most recent discoveries in the following topics: theory-guided synthesis for enhanced control of 2D morphologies, quality, yield, as well as insights toward novel 2D materials; defect engineering to control and understand the role of various defects, including in situ and ex situ methods; and properties and applications that are related to moiré engineering, strain engineering, and artificial intelligence. Finally, we also provide our perspective on the challenges and opportunities in this fascinating field.

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.

Magnons and magnetic fluctuations in atomically thin MnBi2Te4

Electron band topology is combined with intrinsic magnetic orders in MnBi₂Te₄, leading to novel quantum phases. Here we investigate collective spin excitations (i.e. magnons) and spin fluctuations in atomically thin MnBi₂Te₄ flakes using Raman spectroscopy. In a two-septuple layer with non-trivial topology, magnon characteristics evolve as an external magnetic field tunes the ground state through three ordered phases: antiferromagnet, canted antiferromagnet, and ferromagnet. The Raman selection rules are determined by both the crystal symmetry and magnetic order while the magnon energy is determined by different interaction terms. Using non-interacting spin-wave theory, we extract the spin-wave gap at zero magnetic field, an anisotropy energy, and interlayer exchange in bilayers. We also find magnetic fluctuations increase with reduced thickness, which may contribute to a less robust magnetic order in single layers.

MnBi2Te4, referred to as MBT, is a van der Waals material combining topological electron bands with magnetic order. Here, Lujan et al study collective spin excitations in MBT, and show that magnetic fluctuations increase as samples reduce in thickness, implying less robust magnetic order.

Electric control of a canted-antiferromagnetic Chern insulator

The interplay between band topology and magnetism can give rise to exotic states of matter. For example, magnetically doped topological insulators can realize a Chern insulator that exhibits quantized Hall resistance at zero magnetic field. While prior works have focused on ferromagnetic systems, little is known about band topology and its manipulation in antiferromagnets. Here, we report that MnBi₂Te₄ is a rare platform for realizing a canted-antiferromagnetic (cAFM) Chern insulator with electrical control. We show that the Chern insulator state with Chern number C = 1 appears as the AFM to canted-AFM phase transition happens. The Chern insulator state is further confirmed by observing the unusual transition of the C = 1 state in the cAFM phase to the C = 2 orbital quantum Hall states in the magnetic field induced ferromagnetic phase. Near the cAFM-AFM phase boundary, we show that the dissipationless chiral edge transport can be toggled on and off by applying an electric field alone. We attribute this switching effect to the electrical field tuning of the exchange gap alignment between the top and bottom surfaces. Our work paves the way for future studies on topological cAFM spintronics and facilitates the development of proof-of-concept Chern insulator devices.

Exotic states emerge from the interplay between band topology and ferromagnetism, but it remains less known in canted-antiferromagnetic phase. Here, the authors realize a canted-antiferromagnetic Chern insulator in atomically-thin MnBi₂Te₄ with electrical control of chiral-edge state transport.