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The interaction between non-trivial topological states and the magnetic order of intrinsic magnetic topological insulators gives rise to various exotic physical properties, including the quantum anomalous Hall effect and axion insulator. These materials possess great potential applications in low-power topological spintronic devices and topological quantum computation. Since the first intrinsic magnetic topological insulator, MnBi2Te4, was discovered in 2019, this material system has received significant attention from researchers and sparked a research boom. This paper begins with discussing the fundamental properties of MnBi2Te4 and then turns to important research findings related to this intrinsic magnetic topological insulator. Specifically, it focuses on the quantum anomalous Hall effect, axion insulating state, and Majorana zero energy mode exhibited by the MnBi2Te4 series. Furthermore, this paper highlights other research directions and current challenges associated with this material system. Finally, this paper provides a summary and outlook for future research on MnBi2Te4, aiming to offer valuable references for researchers in related fields.
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图 1 磁性拓扑绝缘体奇异拓扑性质及应用前景[23] (a) 量子反常霍尔效应[9]; (b) 轴子绝缘体态[24,25]; (c) 太赫兹辐射[21]; (d) 手性马约拉纳费米子及拓扑量子计算[26]
Figure 1. Singular topological properties and application prospects of magnetic topological insulators[23]: (a) Quantum anomalous Hall effect[9]; (b) axion insulator state with antiparallel magnetization [24,25]; (c) terahertz radiation[21]; (d) chiral Majorana fermions and topological quantum computation[26].
图 2 MBT的晶体结构图[15,29] (a) 由两个SLs组成反铁磁MBT的原子结构图[15]. 每个SL内为铁磁性, 相邻SL之间为反铁磁性. 红色箭头表示Mn原子磁矩; 绿色箭头表示空间平移算符τ1/2; (b) 在Si(111)衬底上生长的5 SLs MBT薄膜的横截面HAADF-STEM图像[29]; (c) HAADF-STEM沿(b)中Cut 1的强度分布图[29]; (d)在Si(111)上生长的MBT薄膜的XRD图[29]
Figure 2. Crystal structure in MBT[15,29]: (a) Atomic structure of MBT consists of two SLs, whose magnetic states are ferromagnetic within each SL and antiferromagnetic between adjacent SLs[15]. The red arrows represent the spin moment of Mn atom. The green arrow denotes for the half translation operator τ1/2; (b) cross-sectional HAADF-STEM image of a 5 SLs MBT films grown on a Si(111) substrate[29]; (c) intensity distribution of HAADF-STEM along Cut 1 in panel (b)[29]; (d) XRD pattern of MBT films grown on Si(111)[29].
图 3 MBT磁相图 (a) MBT薄膜的层数-温度相图[47]; PM代表顺磁区域; A-type AFM代表A型反铁磁区域; (b) 12 SLs MBT/Pt异质结自旋排列随温度和外加磁场的变化[39]; (c) 2 SLs MBT的温度-磁场相图[47]; (d) 3 SLs MBT的温度-磁场相图[47]; 白色圆圈和三角形分别表示在不同温度下计算得到的spin-flop场μ0H1和spin-flip场μ0H2, 即A-AFM/CAFM相和CAFM/FM相的临界转变点; 实验数据点用灰色的球和三角形表示
Figure 3. Magnetic phase diagram of MBT: (a) Layer number-temperature phase diagram of the MBT flake[47]; PM denotes the region where the flake is paramagnetic; A-type AFM denotes the region where adjacent ferromagnetic SLs couple antiferromagnetically with each other; (b) spin configuration of 12 SLs MBT/Pt bilayer as functions of temperature and external magnetic field[39]; (c) temperature-field phase diagram of 2 SLs MBT[47]; (d) temperature-field phase diagram of 3 SLs MBT[47]; the white circles and triangles represent the calculated spin-flop field μ0H1 and spin-flip field μ0H2, respectively, at various temperatures, showing the boundaries of the A-type AFM/CAFM phase and CAFM/FM phase; the experimental data points are represented using grey spheres and triangles with corresponding error bars.
图 4 MBT表面态能带结构图 (a) 保留S对称性的表面具有无能隙的Dirac锥表面态示意图[42]; (b) MBT(011)方向表面 (保持S对称性)的表面态[15,42]; (c) 破坏S对称性的表面具有有能隙的Dirac锥表面态[42]; (d) MBT (111)方向表面(破坏S对称性)的表面态[15,42]
Figure 4. Energy band structure of MBT with surface state: (a) The Dirac surface state is gapless due to the S symmetry[42]; (b) the surface state on MBT(011) with S symmetry[15,42]; (c) the Dirac surface state is fully gapped due to the S symmetry broken[42]; (d) the surface state on MBT(111) without S symmetry[15,42].
图 5 MBT丰富的拓扑量子态 (a) MBT薄膜(2D)和块体(3D)在不同磁化状态下丰富的拓扑量子态. QAH, 量子反常霍尔态; AI, 轴子绝缘体; QSH, 量子自旋霍尔态; TI, 拓扑绝缘体; WSM, Weyl半金属; DSM, Dirac半金属[16,48]. (b) MBT (110)面和 (111)面的无带隙和有带隙表面态能带结构[16,48]
Figure 5. Rich MBT topological quantum states. (a) MBT thin films (2D) and bulk (3D) have rich topological quantum states in different magnetic states. QAH, quantum anomalous Hall state; AI, axion insulator; QSH, quantum spin Hall state; TI, topological insulator; WSM, Weyl semimetal; DSM, Dirac semimetal[16,48]. (b) Surface states of the MBT (110) and (111) surfaces, which are gapless and gapped, respectively[16,48].
图 6 MBT量子反常霍尔效应 (a) 磁性拓扑绝缘体中表面态有带隙的能带结构示意图[24]; (b) 奇数层MBT本征量子反常霍尔绝缘体的示意图[16]; (c) 5 SLs的MBT样品零磁场下的量子反常霍尔效应[31]
Figure 6. Quantum anomalous Hall effect of MBT: (a) Schematic diagram of the energy band structure with a band gap in the surface state in a magnetic topological insulator[24]; (b) illustration of intrinsic QAH insulators in odd layers[16]; (c) quantum anomalous Hall effect under zero magnetic field in 5 SLs MBT[31].
图 8 MBT轴子绝缘体态[16,32] (a) 偶数层MBT本征轴子绝缘体的示意图[16]. 顶部和底部有带隙的表面具有半整数量子化的霍尔电导, 其符号在偶数层中相反, 导致C = 0; (b) 轴子绝缘态的ρxx和
$ \dfrac{{\rm{d}}{\rho }_{yx}}{{\rm{d}}H} $ 与栅极电压的依赖关系[32]; (c) 栅极电压Vg = 25 V时, 不同温度下纵向电阻率和霍尔电阻率随磁场强度的变化关系[32]Figure 8. Axion insulator state in MBT[16,32]: (a) Illustration of intrinsic axion insulators in even layers[16]. The intrinsically gapped surfaces on the top and bottom sides have half-quantized Hall conductances, whose signs are opposite in even layers, leading to C = 0 ; (b) gate dependence of ρxx and
$ \dfrac{{\rm{d}}{\rho }_{yx}}{{\rm{d}}H} $ in axion insulator state[32]; (c) longitudinal and Hall resistivities versus magnetic field strength at various temperatures with gate voltage Vg = 25 V[32].
图 7 MBT高陈数陈绝缘体态 (a) 5 SLs MBT门电压调控的反常霍尔效应[31]; (b) 5 SLs MBT的顶部和底部表面态的示意图[31]; (c) 10 SLs MBT中C = 2的高陈数陈绝缘体态的Ryx和Rxx与磁场和温度间的关系[33]; (d) 具有两个手性边缘态的高陈数陈绝缘态示意图; 灰色和绿色表示相邻SLs的MBT[33]; (e) 铁磁 MBT能带结构示意图, 其为磁性Weyl 半金属[33]; (f) 计算得到的MBT陈数随膜厚的变化函数[33]
Figure 7. High Chern number of Chern insulator MBT. (a) Anomalous Hall effect of 5 SLs MBT by gate voltage[31]. (b) Schematic band diagrams for the top and bottom surface states of this fivelayer sample[31]. (c) Temperature and magnetic field dependence of Ryx and Rxx in high-Chern-number Chern insulator states with C = 2 in 10 SLs MBT device[33]. (d) Schematic of high-Chern-number Chern insulator states with two chiral edge states across the band gap; gray and green indicate adjacent MBT SLs[33]. (e) Schematic diagram of band structure of the ferromagnetic MBT, which is a magnetic Weyl semimetal[33]. (f) Chern number as a function of film thickness in MBT[33].
图 9 MBT马约拉纳特性 (a) 无自旋Kitaev一维p波超导紧束缚链[69]; (b) 环上的拓扑p + ip超导体在其内外边界支持手性马约拉纳边缘模式[74]; (c) 无自旋二维p+ip超导体[75], 三维拓扑绝缘体靠近铁磁体(M↓)和超导体(S)时, 沿超导体和铁磁体边缘出现手性马约拉纳模式; (d) 在AFM TI和s波超导SC之间的界面边缘(灰色)的马约拉纳铰链模式(蓝色和红色箭头)[19]; (e) MBT薄膜与顶部表面的s波超导SC耦合[94]
Figure 9. Majorana characteristics in MBT. (a) Sketch of Kitaev one-dimensional p-wave superconducting tight binding chain without spin[69]. (b) The topological p + ip superconductor on an annulus supports chiral Majorana edge modes at its inner and outer boundaries[74]. (c) Spin free two-dimensional p + ip superconductors[75]. When the three-dimensional topological insulator is close to the ferromagnet (M↓) and superconductor (S), the chiral Majorana mode appears along the edge mode superconductor and ferromagnet. (d) Majorana hinge modes (blue and red arrows) at the interface edge (gray) between an AFM TI and an s-wave superconducting SC[19]. (e) The MBT thin film is coupled to s-wave superconducting SC on the top surface[94].
图 11 (MnBi2Te4)m(Bi2Te3)n体系丰富的拓扑物相 (a) (MnBi2Te4)m(Bi2Te3)n体系拓扑相图[114]. 灰色、黄色和蓝色分别代表平庸的绝缘体、量子自旋霍尔态和量子反常霍尔态; (b) Mn-Bi-Te体系随层间电子耦合和交换作用的不同展现丰富的拓扑物相[115]
Figure 11. Rich topological phase in (MnBi2Te4)m(Bi2Te3)n system: (a) Topological phase diagram in (MnBi2Te4)m(Bi2Te3)n system[114]. Gray, yellow, and blue represent normal insulators, quantum spin Hall states, and quantum anomalous Hall states, respectively; (b) phase diagram of the multilayer topological heterostructure Mn-Bi-Te systems in terms of relative spacing and magnetization[115]
图 12 Mn(Bi1–xSbx)2Te4的丰富物理现象及能带结构 (a) Mn(Bi1–xSbx)2Te4的n-p载流子转变和拓扑相变图[116]; (b) 不同Sb掺杂浓度的Mn(Bi1–xSbx)2Te4样品的ARPES测量的能带结构图[116,129]
Figure 12. Rich physical phenomena and band structure of Mn(Bi1–xSbx)2Te4: (a) n-p carrier transition and topological phase transition diagram of Mn(Bi1–xSbx)2Te4[116]; (b) band structure diagram of ARPES measurement of Mn(Bi1–xSbx)2Te4 samples with different Sb doping concentrations[116,129].
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