1 Introduction

Theoretical predictions and experimental verification are both vital for the search of new materials with new physics and related potential applications. When comes to the magnetic topological insulators (MTI), from the improvement roadmap in the past two decades, one could say the work is challenging and exciting. Earliest first-principles calculations predicted that Cr or Fe doped 3D TI materials Bi2Te3, Bi2Se3 and Sb2Te3 would form the magnetically ordered TI and realize quantum anomalous Hall effect (QAHE) in the systems [1]. Thereafter, tremendous effects have been put into the experimental searching for the suitable materials. After trying almost all 3d transition metals and 4f rare-earth metals, only V and Cr doped Sb2Te3 were found to possess long-range ferromagnetic (FM) order with strong out of plane easy axis anistropy, having potential in realizing QAHE [2, 3]. Fortunately, by accurate control of the growth conditions by molecular beam epitaxy (MBE) technique and precise tuning of the Fermi level (\(E_{F}\)) by applying gate voltage during measurement, QAHE was finally realized in the V, Cr doped (Bi,Sb)2Te3 [4, 5]. However, the realization temperature of QAHE in the system is rather low (∼hundreds of mili-Kelvin) due to high degree of magnetic inhomogeneity and doping induced disorder. The new strategy of raising QAHE temperature by V-Cr codoping [6] or by creating a sandwich with a rich-Cr-doped thin (1 nm) layer at the center and non-Cr-doped (Bi,Sb)2Te3 films at the adjacent were employed to suppress the disorder and improve the QAHE temperature [7], observing QAHE up to 2 K have been achieved, but further great progress in the system seems very difficult. On the other hand, by creating the anti-parallel magnetization in the MTI/TI/MTI heterostructure, the axion insulator state can be realized, manifested by a stable zero Hall plateau state with zero Hall conductivity when the magnetization is antiparallel [8, 9]. It is a novel magnetoelectric response in topological matter. In recent years, the emergence of 2D magnets, which host crystallized intrinsic magnetic order with low level of disorder, were predicted and experimentally realized [10, 11]. These 2D magnets themselves are not topological, platform for interesting physics should be the combination of the non-topological 2D ferromagnetic/antiferromagnetic (FM/AFM) layers with the quasi-2D topological materials. It is of great importance to find a more pristine and controllable platform with low level of disorder for the studies of the exotic topological states arising from the combination of magnetism and topology.

MnBi2Te4, an intrinsic van der Waals antiferromagnetic topological insulator (AFMTI), was successfully predicted and experimentally observed [12–16]. It is a stoichiometric well ordered magnetic compound, in which Mn atoms are ferromagnetically coupled in the intralayer and antiferromagnetically coupled in the interlayers. Bulk MnBi2Te4 shows AFM order [12], magnetic orders in the few-layer samples are found to be strongly layer number dependent-FM order in the odd layer and AFM order in even layer samples [17]. Meanwhile, topological phase transition from topologically trivial monolayer to nontrivial multilayer is revealed by theoretical calculation and confirmed by transport experiment [13, 18]. MnBi2Te4 provides a good playground for research because the topology and magnetism are well combined, which will lead to rich topological properties [19], not only QAHE [20], but more interesting physical properties, for example, topological magnetoelectric effect [14], topological axion state [14], antiferromagnetic topological insulator and Weyl semimetal [15]. Hence, the discovery of AFMTI MnBi2Te4 is really big news in physics and material arena.

In this article, we will give a comprehensive review of the theoretical and experimental progress achieved in MnBi2Te4. Especially, we will focus on the experimental characterization by using different techniques to reveal the various topological quantum properties in this material. Finally, conclusions and perspectives on MnBi2Te4 and the possible proposals are given. It is believed that more impressive work would be made on MnBi2Te4 and would contribute a lot to the topological related applications.

2 MnBi2Te4 crystal growth and structure

Up to now, plenty of researches done on MnBi2Te4 are using the exfoliated 2D layers from the bulk crystal. For these studies, to obtain high quality crystal is rather critical. High quality 3D MnBi2Te4 single crystal can be prepared with solid state reaction, via grown from melt of MnTe and Bi2Te3 [21], or via grown from mixtures of high purity elemental Mn, Bi and Te with certain extra Bi and Te as self-flux [22]. The growth conditions, especially the initial ratio of materials and the temperature control during growth are vital to obtain crystals with high quality because the small energetic difference between the melting temperatures of MnBi2Te4 and Bi2Te3. One could grow high quality several-millimeter-sized thick bulk samples under optimized conditions [22]. Because the layers are separated by van der Waals gaps in bulk MnBi2Te4, the fabrication techniques developed successfully on other 2D materials enables the fabrication of high quality few-layer MnBi2Te4 flakes and devices for rich studies [18, 20, 23, 24]. However, thin flakes by exfoliation method confront big challenges in studies and applications, because the flake shapes are not regular and the thickness is nonuniform. MBE growth has a controllable evaporating speed, meanwhile, precise oscillation with thickness changes during growth process can be monitored by RHEED, it is assumed to be a better way for growing wafer-sized MnBi2Te4 thin films. High quality MnBi2Te4 thin films have been realized through repeated growth of one quintuple-layer (QL) of Bi2Te3 and one bilayer (BL) of MnTe [16] or a co-evaporation of Mn, Bi, Te sources. Thin film sample with uniform layer number can be successfully prepared [25].

MnBi2Te4 crystallizes in a layered structure, the unit cell is rhombohedral with \(\text{R}\bar{3}\text{m}\) space group symmetry, as shown in Fig. 1. The lattice parameter of the unit cell is \(a = b = 4.33~\mathring{\mathrm{A}}\) and \(c = 40.91~\mathring{\mathrm{A}}\) [26]. Usually, one can see this structure in another view, i.e. the hexagonal atom arrangement structure in the ab plane and stack of Te-Bi-Te-Mn-Te-Bi-Te septuple layers (SLs) connected by van der Waals forces along the c axis (Fig. 1(b) and (c)) [25]. The bulk crystal is easily to be cleaved along the two adjacent septuple layers and obtain a Te-terminated surface. One SL has a thickness of ∼1.4 nm, nearly \(1/3\) of the lattice constant c. Recent exploration of MnBi2Te4 have found thickness dependent properties such as magnetic order, electronic structure and topological properties. It is a prerequisite to determine the thickness of samples for such related studies. Transmittance experiments and Atomic Force Microscopy are both powerful means to characterize the sample thickness [17, 20].

Figure 1
figure 1

(a) Unit cell of MnBi2Te4 crystal. The position of atoms is obtained at a temperature of 100 K [22]. (b) and (c) Schematic lattice structures of MnBi2Te4 in the top (b) and side (c) views [25]

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3 Magnetic properties

The magnetic ground state of each septuple layer of MnBi2Te4 is FM due to the strong first nearest exchange interaction between Mn ions. This result is confirmed by high coincidence between experimental spin wave data and theoretical calculation based on Heisenberg model [26]. However, due to the Anderson superexchange, interlayers are coupled antiferromagnetically. The illustration of the AFM magnetic structure of MnBi2Te4 is shown in the left panel of Fig. 2(a). The temperature and field dependent magnetization measurement conducted on MnBi2Te4 single crystals show that MnBi2Te4 establishes a three-dimensional (3D) AFM order with Neel temperature \(T_{N} = 24.2(5)\text{ K}\), in agreement with the simulations [12]. Layer dependent magnetic structure was studied by polar reflective magnetic circular dichroism (RMCD) measurement [17, 27]. It is found that when the sample thickness is reduced, \(T_{N}\) decreases as the number of SL decreases, as seen in Fig. 2(b), the \(T_{N}\) value drops from 24.5 K for a 25-SLs sample, equivalent to the bulk, to 15.2 K for a 1-SL sample. The suppression of \(T_{N}\) can be understood in the frame of thermal fluctuation. Theoretically, due to the Mermin-Wagner theorem, a pure two-dimensional (2D) system or one-dimensional (1D) system cannot have spontaneous symmetry breaking due to the Goldstone mode. However, because the presence of easy-axis magnetic anisotropy and additional contribution of the 3D exchange, the MnBi2Te4 sample still remains magnetic as the sample is approaching 2D limit [13].

Figure 2
figure 2

(a) Schematics of magnetic order evolution as a function of magnetic field. From left to right: AFM, cAFM, and FM states [27]. (b) Layer number-temperature phase diagram of the MnBi2Te4 flakes. PM denotes paramagnetic; A-type AFM denotes the AFM coupled SLs. (c) RMCD measurements of MnBi2Te4 flakes (from 1-SL to 9-SLs) at 1.6 K [17]. The vertical axis is percentage and horizontal axis is magnetic field. The shaded areas highlight the thickness dependence of the low-field spin-flip and spin-flop phase transitions in odd-N and even-N SL samples [17]. (d) and (e) RMCD signal for the 5-SLs and 6-SLs device the AFM state nearly vanishes. The different magnetization states by applying field are indicated by the color bar below the loop [27]

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It is reported that few-layered MnBi2Te4 exhibits an evident odd-even layer-number magnetism, as shown in Fig. 2(c), (d) and (e). The magnetic order of the system exhibits an uncompensated AFM ordering when the number of SL layers is odd and compensated AFM ordering otherwise [13]. Figure 2(c) shows that all measured odd-number (odd-N) SLs show a single hysteresis loop centered at \(\mu _{0}H = 0\text{ Oe}\), indicating its FM feature due to an uncompensated layer. Unexpectedly, an anomalous magnetic hysteresis loop centered at \(\mu _{0}H = 0\text{ Oe}\) in even-number (even-N) SLs MnBi2Te4 is also observed, indicating a net magnetization in the A-type AFM material, which is supposed to be caused by the substrate effect or surface-induced magnetism [20]. However, this origin of anomalous hysteresis loop at zero magnetic field in even-N SLs cases needs further detailed investigation.

The layer-dependent magnetic states can also be manifested by different critical magnetic field for spin-flop. The spin-flop field of the measured odd-N SLs flakes decreases as the number of layers increases and even-N SLs MnBi2Te4 samples show an opposite way. Besides, the critical magnetic field for odd-N SLs system is larger than that for even-N SLs system [27]. In Fig. 2(d) and (e), the magnetization states (including FM, AFM and canted AFM (cAFM) shown in Fig. 2(a)) of the 5-SLs and 6-SLs samples change at each step of the RMCD curves with the external magnetic field. Clearly one can see that the spin-flop of 5-SLs sample is larger than the 6-SLs sample. A linear-chain model was built to understand quantitatively about the spin-flop phenomena. Because the intralayer FM coupling is stronger than interlayer AFM coupling, the linear chain model is assigning “macro spin” to each layer and assuming an exchange interaction J between these “macro spins” [17]. In the uncompensated odd-N SLs samples, the magnetization contributes a Zeeman energy to the total energy under the external magnetic field and results in the higher spin-flop transition field. The magnetic states would greatly affect the transport behavior of different N-SLs samples.

4 Electronic properties

4.1 Electronic band structures

Theoretically, the magnetic order in the topological materials would strongly affect the topological surface states and cause the generation of exotic topological quantum effects. One direct feature is a gap opened on the topological surface state at the Dirac Point. The interconnection between magnetic order and surface states was systematically investigated with spin- and angle-resolved photoemission spectroscopy [12]. Figure 3(a) shows that the MnBi2Te4 (0001) surface band structure possesses two almost linear dispersing bands and forms a Dirac-cone-like structure with strongly reduced intensity at the crossing point. From the second derivative data, one can see the gaped Dirac cone along with the bulk bands. The bulk bandgap and the surface band energy gap are estimated to be 200 meV and 70 meV respectively according to the energy distribution curves (EDCs), which is consistent with the band structure calculations [12].

Figure 3
figure 3

(a) Dispersion of MnBi2Te4 (0001) measured with laser photon energy of 6.4 eV at \(T = 10.5\text{ K}\), the corresponding second derivative is shown in the inset. The dashed rectangle around the Dirac point marks the region that is magnified [12]. (b) Temperature dependence of the Dirac surface state photoemission intensity [12]. (c-h) ARPES measurement under different incident energy and energy distribution curve. The figures (c-e) and figures (g-h) are measured at temperature \(T = 10 \text{ K}\) and the figure (f) is taken at temperature \(T = 80 \text{ K}\) [28]. (i) Energy distribution curves at Γ̄ point [28]

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From the further temperature and photon energy dependent measurements, more could be addressed on the impact of magnetic exchange splitting on the electronic structure [28]. It is found that above \(T_{N}\), the Dirac point gap will not close at MnBi2Te4(0001), however, characteristic signal can give the clue of the FM-AFM transition. The photoemission intensities at the Dirac cone with varying the temperature were extracted and summarized in Fig. 3(b), one can notice the abrupt increase of the intensity, which happens around the \(T_{N}\) of MnBi2Te4.

The bulk valence band (BVB) and bulk conduction band (BCB) at temperature of 10 K and 80 K with different incident photon energies were closely examined, see Fig. 3(c)-(h). First, the \(E_{F}\) lies in the BCB, indicating n doped feature of MnBi2Te4 crystal. Second, it is found that the BCB is composed of two states (S1 and S2) with two dimensional like character [28]. The S1 is viewed as a bulk-like state with a surface-resonance character and the S2 state can be attributed to topological surface state driven by the nontrivial \(Z_{2}\) topology in AFM states. In order to clarify the origin of S1, the temperature dependent energy distribution curves of S1 state is given (Fig. 3(i)) [28]. The increase of full width half maximum of S1 state as temperature increases from 10 K to 80 K is supposed to be driven by exchange splitting of S1 state. Furthermore, Reinert et al. also provide evidence for interconnection between spin-orbital coupling and electronic surface states by spin-resolved ARPES measurement. The result shows the influence of spin-orbital coupling on the surface state and shows Rashba-type spin polarization for S1 state in paramagnetic regime. In their work, the research result shows evidence for exchange interaction and spin orbital coupling on surface state [28]. However, the mechanism of how magnetic order is involved with topological surface state needs more exploration [28].

4.2 Transport studies

The rich magnetic states can also manifest themselves in the transport studies. The quantum transport in MnBi2Te4 was first systematically studied by Deng et al. [20]. Similar to the RMCD signals, the Hall resistance \(R_{xy}\) also shows SLs layer number dependent behaviors. The step features and shapes of the curves are highly consistent with the RMCD loops except for the little discrepancy between the value of the spin-flop field. Transport studies show that in the odd-N and even-N layer samples, different topological quantum states can be observed. In the former case, zero-field QAHE was realized in a 5-SLs specimen at 1.4 K, while in the latter case, an axion insulator state is observed in a 6-SLs device.

To observe the QAHE and axion insulator phase, the \(E_{F}\) should be precisely tuned to the surface Dirac cone gap. The gate voltage of \(-200~V\) is used to obtain the best developed quantization in a 5-SLs device. As shown in Fig. 4(a) and (b), zero field transverse Hall resistance \(R_{xy}\) is reported to be \(0.97\frac{h}{e^{2}}\) concomitant with a longitudinal resistance \(R_{xx}\) of \(0.061\frac{h}{e^{2}}\) at zero magnetic field at the \(T = 1.4\text{ K}\) [20]. More interestingly, by applying external magnetic field, the FM alignment of the 5-SLs would be beneficial to the robustness of QAHE. Under a magnetic field of 7.6 T, when the SLs are fully polarized, the quantilized Hall resistance within a reduction of 3% can be sustained up to 6.5 K, which is record high in the past QAHE researches. Further increasing the magnetic field to the high-field limit, in a 7-SLs device, the zero Hall plateau is observed as seen in Fig. 4(c). At lower magnetic field, the Hall plateaus are strongly dependent on the doping level of the samples, however, when the external field is applied to more than several tens of Tesla, all the plateaus exhibit a strong tendency towards the zero Hall plateau regardless of the position of \(\text{E}_{F}\) [18]. For the axion insulator state, a 6-SLs device is selected for study. As shown in Fig. 4(d), the zero Hall plateau can be observed in zero magnetic field, over a wide magnetic-field range \(-3.5\text{ T} < H < 3.5\text{ T}\) and at relatively high temperatures. Meanwhile, a moderate magnetic field drives a quantum phase transition from the axion insulator phase to a Chern insulator phase with zero longitudinal resistance and quantized Hall resistance of \(\frac{h}{e^{2}}\) [29].

Figure 4
figure 4

(a) Transverse Hall resistance and (b) Longitudinal Hall resistance measured at \(T = 1.4\text{ K}\) in a 5-SLs device [20]. (c) Transport properties of a 7-SLs device in pulsed magnetic field up to 61.5 T [18]. (d) Temperature evolution and quantum critical behaviour of the axion insulator to Chern insulator transition in a 6-SLs device [29]

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Type II weyl semimetal has two signatures in its transport properties: extra quantum oscillation due to the Weyl orbit and anisotropic negative magnetoresistance [30]. The transport measurement on WTe2 provides evidence to support WTe2 as a type-II Weyl semimetal. Similar transport measurement can be done on MnBi2Te4 and successful observation of these two signatures could provide evidences for Weyl semimetal states in MnBi2Te4. The measurement of magnetoresistance was done on 10 to 20 nm MnBi2Te4 thin flakes with external magnetic field parallel and perpendicular to the c axis. Liao et al. observed a transition from negative to positive magnetoresistance as the magnetic field rotating from perpendicular to c axis to parallel [31]. The results of measurement are shown in Fig. 5. The result obtained with the presence of out of plane magnetic field shows evidence that MnBi2Te4 is in Weyl semimetal phase. The inflection point induced by transition from compensated AFM order to FM order. The monotonic increasing of resistance after the inflection point shows a similar case in TaAs family, which is reported to host Weyl semimetal states [32]. The nonsaturated increase of resistance is believed to be similar with the mechanism of weyl semimetal phase. However, the connection behind these two mechanisms needs further confirmation. Besides the sign of magnetoresistance transition, according to the study by Wang et al., another strong feature of FM Weyl semimetals can be demonstrated by the discrete increase of Chern number with increasing film thickness. It is found that in the 7-SLs and 8-SLs MnBi2Te4 devices, the \(R_{xy}\) reaches a well-quantized Hall resistance plateau, while 9-SLs and 10-SLs MnBi2Te4 devices show significant difference with a Hall resistance plateau value of \(\frac{h}{2e^{2}}\). First- principles calculations indicate that high-Chern-number band insulators can be realized in the FM Weyl semimetal MnBi2Te4 by means of quantum confinement [23].

Figure 5
figure 5

(a) Magnetoresistance measured when the external magnetic field is parallel to the c axis under 4 different temperatures [31]. (b) Magnetoresistance measured when the external magnetic field is perpendicular to the c axis under 4 different temperatures [31]

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5 Topological properties

The studies of magnetic and electronic properties, together with the theoretical predictions about MnBi2Te4 are sufficient to give us a picture of the various topological quantum states in this material. Theoretical exploration of thickness dependent topological properties showed a topological phase transition from topologically trivial monolayer to nontrivial states in the multilayer [13]. Thickness dependence of the MnBi2Te4 films topology and band gap size were calculated, the results are shown in Table 1. The system will be in a zero-plateau quantum anomalous Hall (ZPQAH) state (axion state) as the number of SL becomes even and QAH state as the number of SL becomes odd. Take 2-SLs sample for example. If the sample is in the artificial FM order, it would present a QAH state with \(C = 1\) or \(C = -1\), the edge band states will be the 1D chiral mode. If the sample is in the compensated AFM ground state, the edge state will be a fully gaped Dirac spectrum, see Fig. 6. Even-N SLs MnBi2Te4 represents the first example of an intrinsic ZPQAH phase. Transport measurement on MnBi2Te4 revealed field, temperature and carrier dependent Chern insulator phase and existence of chiral edge mode on MnBi2Te4 platform [18, 29].

Figure 6
figure 6

Electronic band structures of the MnBi2Te4 2-SLs-thick film calculated for the (a) FM and (b) compensated AFM states [13]

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Table 1 Thickness dependence of the MnBi2Te4 films topology and band gap size. QAH and ZPQAH stand for the quantum anomalous Hall phase and its zero plateau state, respectively [13]
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After detailed study of bulk crystal’s transport properties, Liu et al. investigated transport properties of exfoliated MnBi2Te4 thin flakes in a magnetic field up to 60 T. Their results show that MnBi2Te4 possesses helical Chern insulator phases. Tuning gate voltage and strength of magnetic field, they found that the sample will go through phase transition from \(C= -3\) to \(C= 2\). It shows that the system has a robust ground state manifested by \(C= 0\), even in high magnetic field, shown in Fig. 7(a) [18].

Figure 7
figure 7

(a) Topological phase diagram. (b) Multiterminal transport measurement under varying external magnetic field from −60 T to 60 T, terminals are labeled with numbers [18]

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This robust ground state with \(C= 0\) can be regarded as a new topological phases with counter-propagating chiral edge states, which is called helical Chern insulator [18]. In order to further confirmed the validity of helical Chern insulator, Liu performed a multiterminal and nonlocal transport measurement on the sample shown in Fig. 7(b). The result confirmed the existence of counter propagating chiral edge mode. The converging resistance measured from nonlocal terminal at \(\frac{1}{8}\frac{h}{e^{2}}\) shows the existence of helical edge transport.

Wang puts a careful explanation. Restricted by inversion and time-reversal symmetry presented in MnBi2Te4 sample with AFM ordering, the sample experiences topological phase transition between \(C= 0\) and \(C=1\). However, breaking the symmetries by introducing external magnetic field will enhance the interlayer coupling and generates dispersive bands along Γ̄-Z̄ direction. The sample at the same time is in FM Weyl semimetal state and the sample has the possibilities to reach high Chern number state. In Wang’s research, a \(C=2\) state with two chiral edge state across the band gap is reached [23]. The temperature dependence measurement shows that high-Chern-number QHE without Landau Levels can hold at temperature of 15 K, which is higher than liquid helium temperature [23].

6 Conclusions and outlook

In this paper, we briefly introduce the researches done on MnBi2Te4, an intrinsic AFM TI found in the latest 4 years. The material arouses so much attention of researches because it is the best platform so far to study exotic topological quantum phenomena, which acquires a clean system with well ordered magnetism and nontrivial topological state. In the very short research period, great works have been done. The crystal structures, magnetic and electronic properties has been well revealed by various techniques like X-ray scattering, RMCD, ARPES and transport etc. MnBi2Te4 is a layered material with rhombohedral \(\text{R}\bar{3}\text{m}\) crystal structure like Bi2Te3. The naturally ordered Mn atoms in the intralayer are ferromagnetically coupled and Mn atoms in the adjacent interlayers are antiferromagnetically coupled. The magnetism in the few layer samples are strongly layer number dependent and the transport measurement on MnBi2Te4 achieves mutual agreement with the magnetic measurement. The odd layer samples present FM order, in such samples, with proper gate voltage and certain temperatures, the QAHE state can be realized; while the even layer samples present AFM order, axion state can be observed. Furthermore, temperature, doping, external field could affect the different topological phases and induce phase transitions in certain conditions. ARPES measurement shows gapped surface state at the Dirac Point of MnBi2Te4, with a signature of the interaction between the magnetism and the topological surface states.

Although much progress have been made on MnBi2Te4 so far, there is still some further research space in the future.

First, on the one hand, it is very important to obtain high quality MnBi2Te4 crystals for the related QAHE, axion insulator phase or Weyl semimetal phase studies. For the sample growth, although the growth conditions are carefully controlled to eliminate the parasitic phases, cation vacancies and antisite defects are inevitable in the crystals. Systematic study of the origin of defects and disorder should be done to further guide the crystal growth optimization in the near future. On the other hand, successful tuning \(E_{F}\) of MnBi2Te4 by Sb doping in Bi cation site has been reported [33], the magnetic and transport properties can also be greatly affected by doping with other certain elements and worth trying. MBE growth has advantages of growing wafer-sized high quality samples. High quality MBE grown Cr-(Bi,Sb)2Te3 samples were the first system to observe QAHE, not the bulk. However, although the MBE film growth work has been reported on MnBi2Te4, the thorough studies on MBE films are lack. More promising, MBE growth of MnBi2Te4 on different substrates like high oriented pyrolytic graphite (HOPG), black phosphrus or other superconducting materials, would cause special substrate effects on the grown films and more fascinating phenomena are anticipated [34, 35].

Second, external compressive and tensile strains are also freedoms to alter the properties of materials. It has been found by Qi et al. that phase transitions and new ground states emerge upon compression in (MnBi2Te4)m(Bi2Te3)n systems [36]. Theoretical calculations show that rich topological phase transitions can be achieved in 2D dialkali-metal monoxides materials by biaxial or unaxial strain [37], it is believed realization of a series of quantum phase transitions among QAHE, axions or Weyl semimetal states could probably be observed in MnBi2Te4 by applying different kinds of strains on the system.

Third, theoretical calculation showed that MnBi2Te4 will be in Weyl semimetal phase under magnetic field perpendicular to the c axis, as shown in Fig. 8 [15]. The first Weyl semimetal was experimentally observed in TaAs with soft x-ray ARPES (SX-ARPES) and ultraviolet angle resolved photoemission spectroscopy on the plane breaking the rotational symmetry [32]. The methodology of observing the signature of Fermi arc is further completed by measurement of TaP [38]. SX-ARPES is sensitive for the bulk electronic band and ultraviolet ARPES is sensitive to the surface states. However, the condition of observing weyl semimetal state is demanding. The system will only present AFM order when the temperature is below Neel temperature \(T_{N} = 24.5\text{ K}\). Furthermore, an external magnetic field above 2.5 T [20] is required in order to align the magnetization of the compound. Because the presence of external magnetic field, the measurement of Fermi arc with ARPES will be challenging.

Figure 8
figure 8

Fermi arc calculated by Li et al. [15]

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Last, for the vast 2D van der Waals materials family, there have always been great interest of stacking different building blocks together. There have been some theoretical and experimental works on the heterostructures of MnBi2Te4 and Bi2Te3 layers or (MnBi2Te4)m(Bi2Te3)n bulk crystals, the magnetic coupling and the electric properties are both altering in the created systems and rich topological phase diagram can be reached [39–43]. These well designed heterostructures supply new platforms for the topological physics study. We believe that combining 2D MnBi2Te4 nano-sheet with 2D magnets, semiconductors, superconductors or other topological materials, will greatly enlarge the research dimensions of MnBi2Te4.