The interplay between magnetism and non-trivial topology in magnetic topological insulators (MTI) is expected to give rise to a variety of exotic topological quantum phenomena, such as the quantum anomalous Hall (QAH) effect and the topological axion states. A key to assessing these novel properties is to tune the Fermi level in the exchange gap of the Dirac surface band. MnBi$_2$Te$_4$ possesses non-trivial band topology with intrinsic antiferromagnetic (AFM) state that can enable all of these quantum states, however, highly electron-doped nature of the MnBi$_2$Te$_4$ crystals obstructs the exhibition of the gapped topological surface states. Here, we tailor the material through Sb-substitution to reveal the gapped surface states in MnBi$_{2-x}$Sb$_{x}$Te$_{4}$ (MBST). By shifting the Fermi level into the bulk band gap of MBST, we access the surface states and show a band gap of 50 meV at the Dirac point from quasi-particle interference (QPI) measured by scanning tunneling microscopy/spectroscopy (STM/STS). Surface-dominant conduction is confirmed below the Néel temperature through transport spectroscopy measured by multiprobe STM. The surface band gap is robust against out-of-plane magnetic field despite the promotion of field-induced ferromagnetism. The realization of bulk-insulating MTI with the large exchange gap offers a promising platform for exploring emergent topological phenomena.
Recently, the intrinsic magnetic topological insulator MnBi2Te4 has attracted enormous research interest due to the great success in realizing exotic topological quantum states, such as the quantum anomalous Hall effect (QAHE), axion insulator state, high-Chern-number and high-temperature Chern insulator states. One key issue in this field is to effectively manipulate these states and control topological phase transitions. Here, by systematic angle-dependent transport measurements, we reveal a magnetization-tuned topological quantum phase transition from Chern insulator to magnetic insulator w…
Magnetic topological insulators (TIs) with nontrivial topological electronic structure and broken time-reversal symmetry exhibit various exotic topological quantum phenomena. The realization of such exotic phenomena at high temperature is one of central topics in this area. We reveal that MnBi6Te10 is a magnetic TI with an antiferromagnetic ground state below 10.8 K whose nontrivial topology is manifested by Dirac-like surface states. The ferromagnetic axion insulator state with Z4 = 2 emerges once spins polarized at field as low as 0.1 T, accompanied with saturated anomalous Hall resistivity …
We construct a continuum model for the Moiré superlattice of twisted bilayer MnBi$_2$Te$_4$, and study the band structure of the bilayer in both ferromagnetic (FM) and antiferromagnetic (AFM) phases. We find the system exhibits highly tunable Chern bands with Chern number up to $3$. We show that a twist angle of $1^\circ$ turns the highest valence band into a flat band with Chern number $\pm1$ that is isolated from all other bands in both FM and AFM phases. This result provides a promising platform for realizing time-reversal breaking correlated topological phases, such as fractional Chern ins…
A striking feature of time reversal symmetry (TRS) protected topological insulators (TIs) is that they are characterized by a half integer quantum Hall effect on the boundary when the surface states are gapped by time reversal breaking perturbations. While time reversal symmetry (TRS) protected TIs have become increasingly under control, magnetic analogs are still largely unexplored territories with novel rich structures. In particular, topological magnetic insulators can also host a quantized axion term in the presence of lattice symmetries. Since these symmetries are naturally broken on the …
Topological states of quantum matter have attracted great attention in condensed matter physics and materials science. The study of time-reversal-invariant (TRI) topological states in quantum materials has made tremendous progress in both theories and experiments. As a great success, thousands of TRI topological materials are predicted through sweeping search. Richer exotic phenomena are expected to appear in magnetic topological materials because of varied magnetic configurations, but this study falls much behind due to the complex magnetic structures and transitions. Here, we predict the tet…
We propose MnBi$_{2n}$Te$_{3n+1}$ as a magnetically tunable platform for realizing various symmetry-protected higher-order topology. Its canted antiferromagnetic phase can host exotic topological surface states with a Möbius twist that are protected by nonsymmorphic symmetry. Moreover, opposite surfaces hosting Möbius fermions are connected by one-dimensional chiral hinge modes, which offers the first material candidate of a higher-order topological Möbius insulator. We uncover a general mechanism to feasibly induce this exotic physics by applying a small in-plane magnetic field to the antifer…
Realizing axion insulator state with a uniform magnetization considerably facilitates experimental explorations of the intriguing topological magnetoelectric effect, a hallmark of three-dimensional (3D) topological insulators (TIs). Through density functional theory calculations and four-band model studies, we find that magnetic ions Cr3+ in monolayer CrI3 and Mn2+ in septuple-layer MnBi2Se4 have opposite exchange couplings to the topological surface states of 3D TI Bi2Se3. As an exciting result of such opposite exchange couplings, axion insulator state is realized by a uniform magnetization i…
The intrinsic antiferromagnetic (AFM) interlayer coupling in two-dimensional magnetic topological insulator MnBi$_2$Te$_4$ places a restriction on realizing stable quantum anomalous Hall effect (QAHE) [Y. Deng et al., Science 367, 895 (2020)]. Through density functional theory calculations, we demonstrate the possibility of tuning the AFM coupling to the ferromagnetic coupling in MnBi$_2$Te$_4$ films by alloying about 50% V with Mn. As a result, QAHE can be achieved without alternation with the even or odd septuple layers. This provides a practical strategy to get robust QAHE in ultrathin MnBi…
MnBi2Te4 and MnBi4Te7 are intrinsic antiferromagnetic topological insulators, offering a promising materials platform for realizing exotic topological quantum states. However, high densities of intrinsic defects in these materials not only cause bulk metallic conductivity, preventing the measurement of quantum transport in surface states, but may also affect magnetism and topological properties. In this paper, we show by density functional theory calculations that the strain induced by the internal heterostructure promotes the formation of large-size-mismatched antisite defect BiMn in MnBi2Te4…
We report direct visualization of spin-flip transition of the surface layer in antiferromagnet MnBi4Te7, a natural superlattice of alternating MnBi2Te4 and Bi2Te3 layers, using cryogenic magnetic force microscopy (MFM). The observation of magnetic contrast across domain walls and step edges confirms that the antiferromagnetic order persists to the surface layers. The magnetic field dependence of the MFM images reveals that the surface magnetic layer undergoes a first-order spin-flip transition at a magnetic field that is lower than the bulk transition, in excellent agreement with a revised Mil…
The intrinsic magnetic topological insulators MnBi$_2$X$_4$ (X = Se, Te) are promising candidates in realizing various novel topological states related to symmetry breaking by magnetic order. Although much progress had been made in MnBi$_2$Te$_4$, the study of MnBi$_2$Se$_4$ has been lacking due to the difficulty of material synthesis of the desired trigonal phase. Here, we report the synthesis of multilayer trigonal MnBi$_2$Se$_4$ with alternating-layer molecular beam epitaxy. Atomic-resolution scanning transmission electron microscopy (STEM) and scanning tunneling microscopy (STM) identify a…
In the newly discovered magnetic topological insulator MnBi$_2$Te$_4$, both axion insulator state and quantized anomalous Hall effect (QAHE) have been observed by tuning the magnetic structure. The related (MnBi$_2$Te$_4$)$_m$(Bi$_2$Te$_3$)$_n$ heterostructures with increased tuning knobs, are predicted to be a more versatile platform for exotic topological states. Here, we report angle-resolved photoemission spectroscopy (ARPES) studies on a series of the heterostructures (MnBi$_2$Te$_4$, MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$). A universal gapless Dirac cone is observed at the MnBi$_2$Te$_4$ t…
Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$, the $n=$~1 and 2 members of a modular (Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disent…
The observation of quantized anomalous Hall conductance in the forced ferromagnetic state of MnBi2Te4 thin flakes has attracted much attentions. However, strong magnetic field is needed to fully polarize the magnetic moments due to the large antiferromagnetic interlayer exchange coupling. Here, we reported the magnetic and electrical transport properties of the magnetic van der Waals MnBi2Te4(Bi2Te3)n (n=1,2) single crystals, in which the interlayer antiferromagnetic exchange coupling is greatly suppressed with the increase of the separation layers Bi2Te3. MnBi4Te7 and MnBi6Te10 show weak anti…
Crystal growth of MnBi$_{2}$Te$_{4}$ has delivered the first experimental corroboration of the 3D antiferromagnetic topological insulator state. Our present results confirm that the synthesis of MnBi$_{2}$Te$_{4}$ can be scaled-up and strengthen it as a promising experimental platform for studies of a crossover between magnetic ordering and non-trivial topology. High-quality single crystals of MnBi$_{2}$Te$_{4}$ are grown by slow cooling within a narrow range between the melting points of Bi$_{2}$Te$_{3}$ (586 °C) and MnBi$_{2}$Te$_{4}$ (600 °C). Single crystal X-ray diffraction and electron m…
The layered MnBi2nTe3n+1 family represents the first intrinsic antiferromagnetic topological insulator (AFM TI, protected by a combination symmetry ) ever discovered, providing an ideal platform to explore novel physics such as quantum anomalous Hall effect at elevated temperature and axion electrodynamics. Recent angle-resolved photoemission spectroscopy (ARPES) experiments on this family have revealed that all terminations exhibit (nearly) gapless topological surface states (TSSs) within the AFM state, violating the definition of the AFM TI, as the surfaces being studied should be -breaking …
Defect-induced displacement of topological surface state in quantum magnet MnBi$_2$Te$_4$
Oak Ridge National Laboratory（橡树岭国家实验室）；University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校）；Forschungszentrum Jülich（于利希研究中心）；Peter Grünberg Institute (PGI-3)（彼得·格林伯格研究所（PGI-3））；Jülich Aachen Research Alliance (JARA), Fundamental of Future Information Technology（于利希亚琛研究联盟（JARA），未来信息技术基础）；Universität zu Köln（科隆大学）；Ames National Laboratory（艾姆斯国家实验室）；Iowa State University（爱荷华州立大学）；Weizmann Institute of Science（魏茨曼科学研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）
Magnetic topological insulators (TI) provide an important material platform to explore quantum phenomena such as quantized anomalous Hall (QAH) effect and Majorana modes, etc. Their successful material realization is thus essential for our fundamental understanding and potential technical revolutions. By realizing a bulk van der Waals material MnBi4Te7 with alternating septuple [MnBi2Te4] and quintuple [Bi2Te3] layers, we show that it is ferromagnetic in plane but antiferromagnetic along the c axis with an out-of-plane saturation field of ~ 0.22 T at 2 K. Our angle-resolved photoemission spect…
Topological quantum materials coupled with magnetism can provide a platform for realizing rich exotic physical phenomena, including quantum anomalous Hall effect, axion electrodynamics and Majorana fermions. However, these unusual effects typically require extreme experimental conditions such as ultralow temperature or sophisticate material growth and fabrication. Recently, new intrinsic magnetic topological insulators were proposed in MnBi2Te4-family compounds - on which rich topological effects could be realized under much relaxed experimental conditions. However, despite the exciting progre…
The recent discovered antiferromagnetic topological insulators in Mn-Bi-Te family with intrinsic magnetic ordering have rapidly drawn broad interest since its cleaved surface state is believed to be gapped, hosting the unprecedented axion states with half-integer quantum Hall effect. Here, however, we show unambiguously by using high-resolution angle-resolved photoemission spectroscopy that a gapless Dirac cone at the (0001) surface of MnBi$_2$Te$_4$ exists between the bulk band gap. Such unexpected surface state remains unchanged across the bulk Néel temperature, and is even robust against se…
Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ ($n=0,1,2,3$) are promising to realize exotic topological states such as the quantum anomalous Hall effect (QAHE) and axion insulator (AI), where the Bi$_2$Te$_3$ layer introduces versatility to engineer electronic and magnetic properties. However, whether surface states on the Bi$_2$Te$_3$ terminated facet are gapless or gapped is debated, and its consequences in thin-film properties are rarely discussed. In this work, we find that the Bi$_2$Te$_3$ terminated facets are gapless for $n \ge 1$ compounds by calculations. Despite …
We propose a realization of chiral Majorana modes propagating on the hinges of a 3D antiferromagnetic topological insulator, which was recently theoretically predicted and experimentally confirmed in the tetradymite-type $\mathrm{MnBi_2Te_4}$-related ternary chalgogenides. These materials consist of ferromagnetically ordered 2D layers, whose magnetization direction alternates between neighboring layers, forming an antiferromagnetic order. Besides surfaces with a magnetic gap, there also exsist gapless surfaces with a single Dirac cone, which can be gapped out when proximity coupled to an $s$-w…
In intrinsic magnetic topological insulators, Dirac surface state gaps are prerequisites for quantum anomalous Hall and axion insulating states. Unambiguous experimental identification of these gaps has proved to be a challenge, however. Here we use molecular beam epitaxy to grow intrinsic MnBi2Te4 thin films. Using scanning tunneling microscopy/spectroscopy, we directly visualize the Dirac mass gap and its disappearance below and above the magnetic order temperature. We further reveal the interplay of Dirac mass gaps and local magnetic defects. We find that in high defect regions, the Dirac m…
The tuning of magnetic phase, chemical potential, and structure is crucial to observe diverse exotic topological quantum states in $MnBi_2Te_4(Bi_2Te_3)_m$ (m = 0, 1, 2, & 3). Here we show a ferromagnetic (FM) phase with a chiral crystal structure in $Mn(Bi_{1-x}Sb_x)_4Te_7$, obtained via tuning the growth conditions and Sb concentration. Unlike previously reported $Mn(Bi_{1-x}Sb_x)_4Te_7$, which exhibits FM transitions only at high Sb doping levels, our samples show FM transitions ($T_C$ = 13.5 K) at 15%-27% doping levels. Furthermore, our single crystal x-ray diffraction structure refinement…
The interplay between band topology and magnetic order could generate a variety of time-reversal-breaking gapped topological phases with exotic topological quantization phenomena, such as quantum anomalous Hall (QAH) insulators and axion insulators (AxI). Here by combining analytic models and first-principles calculations, we predict QAH and AxI phases can be realized in thin film of an intrinsic antiferromagnetic van der Waal material Mn$_2$Bi$_2$Te$_5$. The phase transition between QAH and AxI is tuned by the layer magnetization, which would provide a promising platform for chiral supercondu…
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 the surface states. Here, we theoretically propose that the axion insulators with a simple ferromagnetic configuration, such as MnBi2Te4/(Bi2Te3)n family, provide an ideal playground to realize TME. In a designed triangular prism geometry, all the surface states are magnetically gapped. Under a vertical …
FeTaX2: A ferrimagnetic quantum anomalous Hall insulator
Fudan University（复旦大学）；Shanghai Research Center for Quantum Sciences（上海量子科学研究中心）；Institute for Nanoelectronic Devices and Quantum Computing, Fudan University（复旦大学纳米电子器件与量子计算研究所）；Hefei National Laboratory（合肥国家实验室）
Axion Insulator State in Hundred-Nanometer-Thick Magnetic Topological Insulator Sandwich Heterostructures
Department of Physics, The Pennsylvania State University（宾夕法尼亚州立大学物理系）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）；Materials Research Institute, The Pennsylvania State University（宾夕法尼亚州立大学材料研究所）
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 MnBi$_2$Te$_4$ 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 soon…
We have performed angle-resolved photoemission spectroscopy on (PbSe)5(Bi2Se3)3m, which forms a natural multilayer heterostructure consisting of a topological insulator (TI) and an ordinary insulator. For m = 2, we observed a gapped Dirac-cone state within the bulk-band gap, suggesting that the topological interface states are effectively encapsulated by block layers; furthermore, it was found that the quantum confinement effect of the band dispersions of Bi2Se3 layers enhances the effective bulk-band gap to 0.5 eV, the largest ever observed in TIs. In addition, we found that the system is no …
Defect Engineering for Stabilizing Magnetic and Topological Properties in Mn(Bi1-xSbx)2Te4
Fudan University（复旦大学）；Southeast University（东南大学）；Eastern Institute of Technology（宁波工程学院）；Shanghai Jiao Tong University（上海交通大学）；East China Normal University（华东师范大学）；Chinese Academy of Sciences（中国科学院）
Realizing anomalous Floquet non-Abelian band topology in photonic scattering networks
Zhejiang University（浙江大学）；National University of Defense Technology（国防科技大学）；China Jiliang University（中国计量大学）；University of Birmingham（伯明翰大学）；University of Manchester（曼彻斯特大学）
Three-dimensional (3D) topological Dirac semimetal, when thinned down to 2D few layers, is expected to possess gapped Dirac nodes via quantum confinement effect and concomitantly display the intriguing quantum spin Hall (QSH) insulator phase. However, the 3D-to-2D crossover and the associated topological phase transition, which is valuable for understanding the topological quantum phases, remain unexplored. Here, we synthesize high-quality Na3Bi thin films with R3*R3 reconstruction on graphene, and systematically characterize their thickness-dependent electronic and topological properties by s…
Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we predict that Ta$_2M_3$Te$_5$ ($M=$ Pd, Ni) monolayers can be 2D QTIs with second-order topology due to the double-band inversion. A time-reversal-invariant system with two mirror reflections (M$_x$ and M$_y$) can be classified by Stiefel-Whitney numbers ($w_1, w_2$) due to the combined symmetry $TC_{2z}$. Using the Wilson loop method, we compute $w_1=0$ and $w_2=1…
Two-dimensional electron dispersions with peculiar band crossings provide a platform for realizing topological phases of matter. Here we theoretically show that the $e_g$-orbital manifold of honeycomb-layered transition metal compounds accommodates a plethora of peculiar band crossings, such as multiple Dirac point nodes, quadratic band crossings, and line nodes. From the tight-binding analysis, we find that the band topology is systematically changed by the orbital dependent transfer integrals on the honeycomb network of edge-sharing octahedra, which can be modulated by distortions of the oct…
Electronic band structures dictate the mechanical, optical and electrical properties of crystalline solids. Their experimental determination is therefore of crucial importance for technological applications. While the spectral distribution in energy bands is routinely measured by various techniques, it is more difficult to access the topological properties of band structures such as the Berry phase γ. It is usually thought that measuring the Berry phase requires applying external electromagnetic forces because these allow realizing the adiabatic transport on closed trajectories along which qua…
Spin orbit coupling (SOC) is the key to realizing time-reversal invariant topological phases of matter. Famously, SOC was predicted by Kane and Mele to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene has precluded experimental observation. Here, we exploit a layer-selective proximity effect---achieved via van der Waals contact to a semiconducting transition metal dichalcogenide--to engineer Kane-Mele SOC in ultra-clean \textit{bilayer} graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find th…
We report the appearance of multiple numbers of completely flat band states in an extended Lieb lattice model in two dimensions with five atomic sites per unit cell. We also show that this edge-centered square lattice can host intriguing topologically nontrivial phases when intrinsic spin-orbit (ISO) coupling is introduced in the microscopic description of the corresponding tight-binding Hamiltonian of the system. This ISO coupling strength acts like a complex next-nearest-neighbor hopping term for this model and can be, in principle, tuned in a real-life experimental setup. In the presence of…
In this article we study 3D non-Hermitian higher-order Dirac semimetals (NHHODSMs). Our focus is on $C_4$-symmetric non-Hermitian systems where we investigate inversion ($\mathcal{I}$) or time-reversal ($\mathcal{T}$) symmetric models of NHHODSMs having real bulk spectra. We show that they exhibit the striking property that the bulk and surfaces are anti-PT and PT symmetric, respectively, and so belong to two different topological classes realizing a novel non-Hermitian topological phase which we call a \emph{hybrid-PT topological phases}. Interestingly, while the bulk spectrum is still fully …
Mirror Chern insulators in two-dimensional altermagnetic Tc$_2$Cl$_2$O and Tc$_2$Br$_2$O
School of Physics, Northwest University（西北大学物理学院）；Shaanxi Key Laboratory for Theoretical Physics Frontiers（陕西理论物理前沿重点实验室）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）；Fundamental Discipline Research Center for Quantum Science and Technology of Shaanxi Province（陕西省量子科学与技术基础学科研究中心）
