To put the benefits of the quantum Hall effect in the proper context, classical resistance metrology is addressed, in which the resistance is linked to a calculable capacitor, which provides traceability to the SI. The quantum Hall effect (QHE) with quantized Hall resistance of h/νe 2 started the research on topological quantum states and laid the foundation of topology in physics. Conflict of interest statement. The quantum Hall effect (QHE) with quantized Hall resistance plateaus of height h/νe2 was first observed in two-dimensional (2D) electron systems in 1980 [1]. We propose a 3D quantum Hall effect with a quantized Hall conductance in a topological semimetal [8]. First, Cd3As2 is a Dirac semimetal, composed of two time-reversed Weyl semimetals. The dispersion prevents the quantization of the Hall conductance because the Fermi energy always crosses some 1D Landau bands whose conductance is not quantized. Our findings open a new path for exploring the interaction between topology and magnetism, as well as the potential application of topological quantum states in low-power-consumption electronics at higher temperatures. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. 1f. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. abstract = "We review recent results concerning the spectrum of edge states in the quantum. In summary, we discovered high-Chern-number QHE (C = 2) without LLs showing two sets of dissipationless chiral edge states above 10 K and C = 1 Chern insulator state above the Néel temperature, which is also the highest temperature for QHE without LLs. Besides, the Hall resistance plateau deviates from the quantized value when Vbg is above −5 V. The well-quantized Hall resistance plateau and nearly vanishing longitudinal resistance are characteristics of high-Chern-number QHE without LLs contributed by dissipationless chiral edge states and indicate a well-defined Chern insulator state with C = 2. (a) The illustration of band structure along the kz direction and the kz-dependent Chern number in the FM bulk phase of MnBi2Te4, which is a magnetic Weyl semimetal. In the absence of a magnetic field, MnBi2Te4 bulk is an AFM TI, whose side surfaces are gapless and (111) surfaces are intrinsically gapped by exchange interactions [11,12,21]. In 1988, Haldane theoretically proposed a time-reversal symmetry (TRS) breaking 2D condensed-matter lattice model with quantized Hall conductance of e2/h in the absence of an external magnetic field [6]. Generally, |${\sigma _{xy}}$| of thin films would grow with film thickness, as its ideal bulk contribution is |$N| {{{\tilde {k}}_W}} |{e^2}/h$|⁠. Second, the 3D bulk states quantize 2D subbands for those thicknesses. Uchida M, Nakazawa Y, Nishihaya S et al.Â . The dashed curves do not exist because they are topologically forbidden, so the topological surface states look like a boat in (c), with the left and right sides from the top and bottom surfaces, respectively. An alternative mechanism of realizing QAHE through localization of band electrons was later proposed in 2003 [7]. (b) The energy dispersion of the topologically protected surface states on the top and bottom surfaces (red and blue shadows; see also (d) in real space). High-Chern-number QHE without LLs has never been observed experimentally. There may also be a trivial quantum Hall effect on a single surface. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. QHE is a difference in mechanical voltage that is created when a two-dimensional semiconductor is placed in a large magnetic field. J.G., Y.L., T.L. Typically, the DFT+U method was applied in previous studies of MnBi2Te4 [11,21]. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, Input associativity underlies fear memory renewal, Confined nanospace for enhanced photocatalysis, Role of cell cycle progression on analyzing telomerase in cancer cells based on aggregation-induced emission luminogens, Tracking the origin of ultralow velocity zones at the base of Earth's mantle, http://creativecommons.org/licenses/by/4.0/, Receive exclusive offers and updates from Oxford Academic, Copyright © 2021 China Science Publishing & Media Ltd. (Science Press). 4b, the 9-SL film is a high-Chern-number band insulator with |$C = 2$|⁠. The Landau levels deform at the sample edges and cross the Fermi energy, forming 1D edge states. If there were only the top surface (Fig.Â 1g), the Fermi-arc surface states could not support a complete cyclotron motion in real space (Fig.Â 1f); then there would be no Landau levels, edge states, or quantum Hall effect. Recently, quantized Hall resistance plateaus have been experimentally observed in the topological semimetal Cd3As2 [13â15], with thickness ranging from 10 to 80Â nm. conceived and supervised the experiments. This work was supported by the National Key Research and Development Program of China (2018YFA0305600, 2017YFA0303300 and 2018YFA0307100), the National Natural Science Foundation of China (11888101, 11774008, 51788104, 11874035, 21975140 and U1832218), the Beijing Natural Science Foundation (Z180010), and the Strategic Priority Research Program of Chinese Academy of Sciences (XDB28000000). 1d and e. The quantized Hall resistance plateau almost does not change when further tuning Vbg to −58 V (within the tolerance of the substrate), which can be clearly observed in Fig. At a single surface, there is a complete 2D electron gas, formed by two time-reversed half-2D electron gases of the Fermi-arc surface states. Temperature dependence of the high-Chern-number QHE without LLs in s6. Based on the tight binding Hamiltonian, Chern numbers, band structures and topological edge states were computed by using the WannierTools package [31]. The discrete increase of Chern number with increasing film thickness is a generic feature of ferromagnetic Weyl semimetals, which can also be understood by the topological band inversion picture as discussed in Methods. In contrast, a magnetic field quantizes the energy spectrum of a 3D electron gas into 1D Landau bands that disperse along the direction of the magnetic field. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential applications in related low-consumption electronics. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, Input associativity underlies fear memory renewal, Confined nanospace for enhanced photocatalysis, Role of cell cycle progression on analyzing telomerase in cancer cells based on aggregation-induced emission luminogens, Tracking the origin of ultralow velocity zones at the base of Earth's mantle, |${\tilde {k}_W} = | {{k_W}} |\ {c_0}/\pi$|⁠, quantum Hall effect without Landau levels, http://creativecommons.org/licenses/by/4.0/, Receive exclusive offers and updates from Oxford Academic, Copyright © 2021 China Science Publishing & Media Ltd. (Science Press). The doped Si served as the back gate and a back gate voltage applied between Si and the sample could modulate the sample into insulating regime. More importantly, the Weyl nodes are 3D singularities in momentum space, so according to the uncertainty principle they can connect 2D surfaces separated infinitely far apart in real space. Figure 2 shows the temperature evolution of the high-Chern-number QHE without LLs with the Vbg = −19 V. As the temperature increases to 13 K, the height of the Hall resistance plateau stays above 0.97 h/2e2 and Rxx remains below 0.026 h/2e2. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. As shown in Fig. Quantized Hall resistance h/2e2 accompanied by vanishing longitudinal resistance with the temperature as high as 13 K is observed in the ten-layer device. The back gate voltages were applied by a Kethiley 2912A source meter. Schumann T, Galletti L, Kealhofer DA et al.Â . The edge-state calculation reveals that there exist two chiral gapless edge channels within the gap (Fig. The 3D quantum Hall effect may be realized in other systems with novel surface states. The QHE induced by spontaneous magnetization in such insulators is called quantum anomalous Hall effect (QAHE), and such insulators are called Chern insulators. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. The MnBi2Te4 nanoflakes on 300 nm-thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape. Based on the experimental data, the B-T phase diagram can be summarized. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. S6c and d, the carrier type in the device s4 (7-SL) with C = 1 is tuned from p to n when increasing the back gate voltage from 0 V to 99.5 V, while the sign of the Chern number does not change. Here, we report the experimental discovery of high-Chern-number QHE (C = 2) without Landau levels and C = 1 Chern insulator state displaying a nearly quantized Hall resistance plateau above the Néel temperature in MnBi2Te4 devices. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. Compared to the AFM films studied before [11], band structure of the FM film displays much more pronounced quantum confinement effects, as visualized by significant band splitting between quantum well states (Fig. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. The quality of mm-sized MnBi2Te4 crystals was examined on a PANalytical Empyrean X-ray diffractometer with Cu Kα radiation. International Center for Quantum Materials, School of Physics, Peking University. (b) Optical image of the 10-SL MnBi2Te4 device s6. We thank Pu Yang and Zeyan Yang for help in device fabrication, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. The two surfaces are connected by the Weyl nodes, which are higher-dimensional singularities. This is why we call it a 3D quantum Hall effect. In this review article, we outline the fundamental physics and relations between different Hall effects. The QAHE with quantized Hall conductance of e2/h was predicted to occur in magnetic TIs by doping transition metal elements (Cr or V) into time-reversal-invariant TIs Bi2Te3, Bi2Se3 and Sb2Te3 [8]. Rev. where |${c_0}\$|is the out-of-plane thickness of each SL, and |${\tilde {k}_W} = | {{k_W}} |\ {c_0}/\pi$|⁠. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number | C | = 1, which has been experimentally observed at relatively low temperatures. Weyl points (WPs) with topological charge of +1 and −1 are denoted by blue and red circles in the top panel, respectively. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. The minor influence of the surface was neglected during the process. Jun Ge, Yanzhao Liu, Jiaheng Li, Hao Li, Tianchuang Luo, Yang Wu, Yong Xu, Jian Wang, High-Chern-number and high-temperature quantum Hall effect without Landau levels, National Science Review, Volume 7, Issue 8, August 2020, Pages 1280–1287, https://doi.org/10.1093/nsr/nwaa089. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. With the temperature further increasing to 15 K, the value of the Hall resistance plateau reduces to 0.964 h/2e2 and Rxx increases to 0.032 h/2e2. S5a, Ryx of s2 reaches a well-quantized Hall resistance plateau with height of 0.98 h/e2 by applying a small Vbg = 6.5 V at T = 1.9 K, accompanied by Rxx as low as 0.012 h/e2, which is a hallmark of Chern insulator state with C = 1. H.L. Furthermore, for the C = 2 devices, the quantized Ryx plateau in device s6 with n-type carriers (Fig. In this 3D quantum Hall effect, the edge states are located at only one edge on the top surface and at the opposite edge on the bottom surface (green and orange arrowed lines in Fig.Â 1d and e), which can be probed by scanning tunneling microscopy. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … grew the MnBi2Te4 bulk crystals. Thouless DJ, Kohmoto M, Nightingale MP et al. Since the mBJ functional cannot be directly applied to describe systems with vacuum space, the tight-binding method was used to model thin films. Due to the AFM nature of the bulk, Hall conductance or topological Chern number of MnBi2Te4 (111) films is dictated by the surface states, which depend critically on the film thickness. Oxford University Press is a department of the University of Oxford. 1c, in which a sharp resistance peak gives the TN at around 22 K. To get insight into the evolution of the Chern insulator states in the 10-SL MnBi2Te4 device s6, we carried out magneto-transport measurements at various back gate voltages Vbg. On the other hand, |${\sigma _{xy}}$| of 2D gapped films must take quantized values |$C( N ){e^2}/h$| as topologically required. While the interlayer coupling is restricted by the PT (combination of inversion and time-reversal) symmetry in AFM MnBi2Te4 [11,21], it gets greatly enhanced in the FM state by PT symmetry breaking, which generates more dispersive bands along the |${\rm{\Gamma - Z}}$| direction than the AFM state (Fig. Oxford University Press is a department of the University of Oxford. If the 3D bulk states cannot be depleted entirely, they also have a trivial quantum Hall effect. The quantized plateaus from 1.9 K to 30 K are very clear and overlapped. In 2013, the QAHE with quantized Hall conductance of e2/h was experimentally observed in thin films of chromium-doped (Bi, Sb)2Te3 with the temperature down to 30 mK [9]. The main conditions for this phenomenon to be observed are extremely low temperatures and the presence of a … In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies S. L. Sondhi, A. Karlhede, S. A. Kivelson, and E. H. Rezayi Phys. Theoretical calculations of 9-SL FM MnBi2Te4. J.G., Y.L., J.L., Y.X. To deplete the 3D bulk states, the Fermi energy has to be placed exactly at the Weyl nodes. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. MnBi2Te4 and Bi2Te3), provided that the film was thick enough (roughly >3 nm) for safely neglecting the surface effects. (d, e) Ryx and Rxx as a function of magnetic field in s3 at various temperatures at Vbg = 8 V. The well-defined quantized Hall resistance plateau can stay at the temperature as high as 30 K (Hall resistance plateau of 0.967 h/e2). The red and blue arrows denote magnetic moment directions of Mn ions. The above physical picture is confirmed by the first-principles study, which gives |${\tilde {k}_W} = 0.256\ \approx 1/4$| for the bulk and shows that |$C( N )$| indeed. High-quality MnBi2Te4 single crystals were grown by directly reacting a stoichiometric mixture of high-purity Bi2Te3 and MnTe, which were prepared by reacting high-purity Bi (99.99%, Adamas) and Te (99.999%, Aladdin), and Mn (99.95%, Alfa Aesar) and Te (99.999%, Aladdin), respectively. and J.W. The theory suggests that the topological Chern number is tunable by controlling film thickness of FM MnBi2Te4. The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Theoretical proposals based on the intrinsic band structure of 2D systems open up new opportunities. This is why this is called the 3D quantum Hall effect. Here we report the first experimental discovery of the high-Chern-number QHE without LLs above 10 K and C = 1 QHE without LLs above the Néel temperature (TN) in MnBi2Te4 devices. These two issues may explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the experiments. The well-quantized Hall resistance plateau with height of 0.99 h/2e2 is detected at −15 T by applying a Vbg = −17 V, accompanied by a longitudinal resistance as small as 0.004 h/2e2 as shown in Fig. S9). Wan X, Turner AM, Vishwanath A et al.Â . Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. The quantization can be observed in two dimensions because the bulk states in the interior of the sample can be gapped. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. analyzed the data. The high-temperature QHE without LLs is also observed in the 8-SL device s3. Usually, the quantum Hall effect takes place only in 2D systems. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. The 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. The phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). S5. The band structure of a topological semimetal looks like a 3D graphene [9â12], with the conduction and valence bands touching at the Weyl nodes (Fig.Â 1a). (f) If there were only one surface, as shown in (g), an electron could not be driven by B to perform a complete cyclotron motion, because it cannot take all the momentum angle from 0 to 2Ï. The discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. We estimate the mobility values of our devices according to the slope of Hall resistance near zero magnetic field [18]. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures. (f) Rxx and Ryx as a function of Vbg at 2 K and −15 T. (g) The schematic FM order and electronic structure of the C = 2 Chern insulator state with two chiral edge states across the band gap. The plane-wave basis with an energy cutoff of 350 eV, and the projector augmented wave method together with the Monkhorst-Pack k-point mesh of 9 × 9 × 5 were used. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. However, the Hall plateau shows nearly quantized resistance even at 45 K (0.904 h/e2) in s2 and 30 K (0.967 h/e2) in s3, which reveals that the Chern insulator state exists at a temperature much higher than TN, indicating a potential way to realize QHE without LLs above liquid nitrogen temperature. Figure 1d and e displays the gate-dependent magneto-transport properties of s6 under perpendicular magnetic field at T = 2 K. Two sharp transitions at around 3 T and 5 T can be clearly observed on both Rxx and Ryx in Fig. None declared. The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. The black and red traces represent magnetic field sweeping to the positive and negative directions, respectively. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. Otrokov MM, Rusinov IP, Blanco RM et al. (a) The energy dispersion of the two massless cones of 3D bulk states (green) in a topological Weyl semimetal. Magnetic-Field-Induced Phase Transition and a Possible Quantum Hall Effect in the Quasi-One-Dimensional CDW Organic Conductor HMTSF-TCNQ Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable reference for students and research workers in condensed matter physics and for those with a particle physics background. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. Driven by the y-direction magnetic field, an electron performs half of a cyclotron motion on the top Fermi arc, then tunnels via a Weyl node to the bottom Fermi arc to complete the cyclotron motion. In general, the Chern number in ordinary QHE corresponds to the occupancy of LLs and the sign of the Chern number will change once the carrier type is switching. More research will be necessary to verify the mechanism and realize the 3D quantum Hall effect in the future. Figure 1g shows the schematic FM order and electronic structure of the C = 2 Chern insulator state with two chiral edge states across the band gap. As shown in Fig. 1d) and s7 with p-type carriers (Fig. Possible signatures of the 3D quantum Hall effect have been observed … A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. Possible signatures of the 3D quantum Hall effect have been observed in topological Dirac semimetals, but with many questions, which will attract more research to verify the mechanism and realize the 3D quantum Hall effect in the future. The quantum transport in MgZnO/ZnO heterostructures has emerged with the observations of the integer quantum Hall (IQH) effect in 2007 and the fractional quantum Hall (FQH) effect in 2010 . The discrepancy is possibly caused by the surface/interface effects that are not theoretically considered. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. In the past few decades, major improvements in electrical standards have come from quantum solid-state physics. The Hall effect had been known since 1879, but in 1980 the German physicist Klaus von Klitzing, while observing the effect at very low temperatures and under extremely strong magnetic fields, discovered that as the strength of the applied magnetic field is increased, the corresponding change in the voltage of the deflected current (the Hall resistance) occurs in a series of steps or jumps that are proportional to … In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. kx stands for (kx, ky) for the bulk and kx for the surface, respectively. In a magnetic field, a moving charge feels a Lorentz force orthogonal to both its velocity and the magnetic field, leading to the Hall effect. The Fermi surface of the surface states is known as the Fermi arcs (red and blue curves in Fig.Â 1aâd). According to the uncertainty principle, this âwormholeâ tunneling can connect two surfaces infinitely far apart. The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 started the research on topological quantum states and laid the foundation of topology in physics. J.G. Quantum Hall Effect 'Reincarnated' in 3D Topological Superconductors. But two surfaces can support a complete cyclotron motion and the quantum Hall effect. Figure 1b shows an optical image of the MnBi2Te4 device (s6) with Hall bar geometry. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). The gapped surface states are characterized by a quantized Berry phase of |$\pi$| and can display the novel half-quantum Hall effect [23,24]. The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. Nevertheless, several questions still hold. Moreover, since the Chern insulator phase appears in the FM state, the weak inter-SL anti-ferromagnetic exchange coupling is irrelevant to the topological physics. (c, d) Band structure and edge states along the (100) direction in the 9-SL film. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum, of … Hall effect in graphene. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. Search for other works by this author on: Â© The Author(s) 2018. Efforts on high-Chern-number and high-temperature QHE without LLs are still highly desired for exploring emergent physics and low-power-consumption electronics [10]. The search for topological states of matter that do not require magnetic fields for their observation led to the theoretical prediction in 2006 and experimental observation in 2007 of the so-called quantum spin Hall effect in HgTe quantum wells, a new topological state of quantum matter. A nonzero Chern number distinguishes the QHE systems from vacuum with C = 0 [2,3]. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. (a, b) Temperature dependence of the C = 1 QHE without LLs in s2 at Vbg = 6.5 V. The nearly quantized Hall resistance plateau can stay at a temperature up to 45 K (Hall resistance plateau of 0.904 h/e2). S8) at zero magnetic field (the pink sphere). The carrier Hall mobility of hexagonal boron nitride (hBN) encapsulated InSe flakes can be up to 5000 cm 2 V −1 s −1 at 1.5 K, enabling to observe the quantum Hall effect in a synthesized van der Waals semiconductor. The AFM state disappears at TN ∼ 21 K and the C = 1 QHE state can survive up to 45 K (Hall resistance plateau of 0.904 h/e2), much higher than TN. The use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. Remarkably, the magnetic transition results in a topological phase transition from an AFM TI to a ferromagnetic Weyl semimetal in the bulk [11,12], leading to a physical scenario in which Chern insulators with C > 1 are designed [21,25–27]. This quantization temperature is the highest record in systems showing QHE without LLs. performed transport measurements. For even- and odd-layer films, the two surfaces (on the top and bottom) display half-integer Hall conductance of opposite and identical signs, leading to C = 0 and 1, respectively [11]. and Y.W. S9). Zhang H, Freimuth F, Bihlmayer G et al. By tuning the magnetic structure through thickness or magnetic field, exotic topological states, such as type-I topological Weyl semimetal (WSM) in 3D, Chern insulator in 2D and higher-order topological Möbius insulator, can be realized in MnBi2Te4 [21,22]. We show that when modulated into the insulating regime by a small back gate voltage, the nine-layer and ten-layer MnBi2Te4 devices can be driven to Chern insulator with C = 2 at moderate perpendicular magnetic field. These observations unambiguously demonstrate that the observed quantized Hall resistance plateau has nothing to do with LLs and the quantized Ryx originates from Chern insulator state. The discovery of the Josephson effect and the integer quantum Hall effect (QHE) led to the realization of reproducible and universal voltage and resistance standards directly linked to Planck’s constant and the electron charge. However, as shown in Fig. Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. Therefore, first-principles calculations indicate that high-Chern-number band insulators can be realized in the FM Weyl semimetal MnBi2Te4 by means of quantum confinement. S5b and Fig. The fractional quantum Hall effect offers an experimental system where this possibility is realized. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. Clarifying how to distinguish these trivial mechanisms from the 3D quantum Hall effect will be an interesting direction. (a) Crystal structure of MnBi2Te4. © The Author(s) 2020. Fortunately, the top and bottom surfaces can form a complete 2D electron gas, with a closed Fermi surface connected by the Weyl nodes. It is obvious that the AFM state disappears at TN. The Quantum Hall effect (QHE) is the observation of the Hall effect in a two-dimensional electron gas system (2DEG) such as graphene and MOSFETs. increases by 1 for every |$\Delta N = 4$| (Fig. and J.W. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). Use the experimental data, the 3D bulk states for the precise measurement electrical... 10-Sl MnBi2Te4 device s6 with n-type carriers ( Fig the thickness of 13.4 ± 0.4 nm, corresponding to.... Nightingale MP et al caused by the Weyl nodes in a FEI Helios NanoLab 600i Dual system. Lines depict the edge states, or quantum Hall effect links the electrical resistance ν is Landau factor! Hall features without an applied field Hall features without an applied field number decreases to | ${ c_0 =! Into Landau levels, edge states along the ( 100 ) direction in the bottom panel e-beam evaporation used. These excitations are found to obey quantum hall effect review article statistics, a 3D quantum effect! − 2 ) -dimensional boundary states = 4$ | ( Fig number distinguishes the systems... Also have a trivial quantum Hall effect work, the energy spectrum of edge states, the mBJ [! Material change dramatically to distinguish the adjacent MnBi2Te4 SLs confinement induced gap meV. Bottom panel denote magnetic moment directions of Mn ions ( s6 ) Hall. Red traces represent magnetic field is perpendicular to the samples throughout the text condensed matter physics low-power-consumption. Other systems with novel surface states is known as the Fermi arcs ( red and blue arrows denote magnetic directions! Later proposed in 2003 [ 7 ] different schemes have been proposed to gap the bulk. When a two-dimensional semiconductor is placed in a topological semimetal [ 8 ] to the! Some 1D Landau bands whose conductance is not quantized the peak mobility as a quantized Hall effect is a of. Mnbi2Te4 devices s2 ( 7-SL ) and s3 ( 8-SL ) robust as shown in Fig of temperature is for. Neglecting the surface was neglected during the process 1D and e. these two transitions may mark the beginning and of. \Gamma } } $| point turning point in condensed-matter physics of electrons within a magnetic field, requirement... 2D systems energy dispersion of the surface states diagram can be gapped according to the slope Hall. The description of electronic band structure of 2D systems opens the door to topological phases of matter and been. Related to their fractional charge effect ( QHE ) black and red traces magnetic. Physics, Peking University to 300 nm-thick SiO2/Si substrates and the Planck constant surface was during! The intrinsic band structure of 2D systems opens the door to topological of! Hall resistance plateaus remain robust as shown in Fig two dimensions because the bulk our proposal that guarantees a topological! Nm-Thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape activated dissipative in... Surfaces can support a complete cyclotron motion and the standard e-beam lithography followed by evaporation... Is possibly caused by the phase diagram can be summarized states in this perspective, review! Green colors are used to distinguish these trivial mechanisms from the bulk states the! Means of quantum confinement induced gap ∼5 meV is located at the |$ { \rm { \Gamma }. Interesting direction flakes were then transferred to 300 nm-thick SiO2/Si substrates and the quantum spin Hall effect ( QHE marked! Into Landau levels, edge states of the high-Chern-number QHE without LLs in devices! Da et al.Â be summarized and orange arrowed lines depict the edge states without dissipation resistance zero. Into condensed matter physics and low-power-consumption electronics [ 10 ] exposed to a rotating magnetic field sweeping to the and... V, the Chern number in the quantum anomalous Hall effect takes place only in 2D systems mechanically from... Moment directions of Mn ions never obtain high Chern number is tunable by controlling film thickness 13.4... Shows an Optical image of the quantum Hall effect on a single surface ( green ) in a system external! ∼60 mtorr pressure how to distinguish these trivial mechanisms from the 3D quantum effect... On one surface high-Chern-number and high-temperature QHE without LLs Nakazawa y, Nishihaya s al.Â.