2$|⁠), which is awaiting experimental confirmation. Furthermore, for the C = 2 devices, the quantized Ryx plateau in device s6 with n-type carriers (Fig. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 1f. 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. Thouless DJ, Kohmoto M, Nightingale MP et al. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … and Y.L. The band structure of a topological semimetal looks like a 3D graphene [9–12], with the conduction and valence bands touching at the Weyl nodes (Fig. 1a). The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. The minor influence of the surface was neglected during the process. grew the MnBi2Te4 bulk crystals. It represents good example of physical systems where quantization effect could be observed microscopically as a result of the interplay of the topology, interactions of electron with magnetic field, electron-electron interactions, and disorder. 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 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. 1d and e), which can be probed by scanning tunneling microscopy. The AFM state disappears at TN ∼ 22.5 K and the well-defined quantization can stay till 30 K (Hall resistance plateau of 0.967 h/e2). In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. High-Chern-number QHE without LLs has never been observed experimentally. and Y.W. The red and blue arrows denote magnetic moment directions of Mn ions. The phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). According to the uncertainty principle, this ‘wormhole’ tunneling can connect two surfaces infinitely far apart. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. Electrons can flow through the edge states without dissipation. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. 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. 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). J.G. This is why we call it a 3D quantum Hall effect. Schumann T, Galletti L, Kealhofer DA et al. . Find methods information, sources, references or conduct a literature review … (c, d) Band structure and edge states along the (100) direction in the 9-SL film. S4a) have the same sign. This indicates that QHE can be realized without the formation of LLs. However, in the above-mentioned QHE systems without LLs, only a Hall resistance plateau with C = 1 can be obtained by coupling topological surface states with magnetism. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. 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. Furthermore, the high-Chern-number QHE without LLs has also been detected in two more 9-SL devices (Figs S2–4). Second, the 3D bulk states quantize 2D subbands for those thicknesses. Thus, the working temperature of QHE without LLs will not be limited by the Néel temperature, and can be quite high due to the strong, ordered magnetism of MnBi2Te4. fabricated devices. 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. Klaus von Klitzing discovered that in strong magnetic fields the Hall resistance of a 2D electron gas can be quantized into a series of plateaus in terms of (h/e2)/n [1], where e is the elementary charge, h is Planck’s constant, and n is an integer known as the ‘Chern number’ (named after the mathematician Shiing-Shen Chern). (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. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. To deplete the 3D bulk states, the Fermi energy has to be placed exactly at the Weyl nodes. Hannahs ST, Brooks JS, Kang W et al. . 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. 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. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. and J.W. This work was supported by the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the National Key R&D Program (2016YFA0301700), the National Natural Science Foundation of China (11574127), and the Science, Technology, and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217, JCYJ20170412152620376). For full access to this pdf, sign in to an existing account, or purchase an annual subscription. The conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … 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. Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator … The results are so precise that the standard for the measurement of electrical resistance uses the quantum Hall effect, which also underpins the … The back gate voltages were applied by a Kethiley 2912A source meter. News. Subsequently, the exact quantization was explained by Laughlin based on gauge invariance and was later related to a topological invariance of the energy bands, which is characterized by Chern number C [2–5]. Theoretical calculations of 9-SL FM MnBi2Te4. This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. Nevertheless, several questions still hold. S8) at zero magnetic field (the pink sphere). We thank Pu Yang and Zeyan Yang for help in device fabrication, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. 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. Usually, the quantum Hall effect takes place only in 2D systems. 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 QHE induced by spontaneous magnetization in such insulators is called quantum anomalous Hall effect (QAHE), and such insulators are called Chern insulators. Search for other works by this author on: © The Author(s) 2018. This working temperature of the high-Chern-number QHE without LLs is much higher than liquid helium temperature, which shows potential application of QHE in low-dissipation electronics. The BAFM (T) data points, as the boundary of the AFM states, are composed of the peak values of the Rxx (B) curves (Fig. S5b). H.L. Typically, the DFT+U method was applied in previous studies of MnBi2Te4 [11,21]. 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. If there were only the top surface (Fig. 1g), the Fermi-arc surface states could not support a complete cyclotron motion in real space (Fig. 1f); then there would be no Landau levels, edge states, or quantum Hall effect. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. The quantum Hall effect is usually observed in 2D systems. We propose a 3D quantum Hall effect with a quantized Hall conductance in a topological semimetal [8]. 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. 4b). The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. 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. 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. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. J.W. 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. 1d and e. These two transitions may mark the beginning and ending of the spin-flipping process. Since the mBJ functional cannot be directly applied to describe systems with vacuum space, the tight-binding method was used to model thin films. 3d and e, Ryx of s3 is 0.997 h/e2 at 1.9 K (Rxx ∼ 0.00006 h/e2), 8 V, and even at 30 K (above Néel temperature TN = 22.5 K), Ryx can reach 0.967 h/e2 (Rxx ∼ 0.0023 h/e2). wrote the manuscript with input from all authors. 4c). DOI: 10.4236/jmp.2013.411A1003 3,240 Downloads 4,702 Views Citations This article belongs to the Special Issue on Advances in Quantum Physics. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. (a) The energy dispersion of the two massless cones of 3D bulk states (green) in a topological Weyl semimetal. S5. (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 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. 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. Abstract. 1a. To obtain flakes with thickness down to several nanometers, we heated the substrate after covering the scotch tape at 393 K (120°C) for one minute. Störmer HL, Eisenstein JP, Gossard AC et al. . kx stands for (kx, ky) for the bulk and kx for the surface, respectively. First-principles calculations were performed in the framework of density functional theory (DFT) by the Vienna ab initio Simulation Package (VASP) [30]. 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. Search for other works by this author on: State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, School of Materials Science and Engineering, Tsinghua University, Tsinghua-Foxconn Nanotechnology Research Center and Department of Physics, Tsinghua University, Department of Mechanical Engineering, Tsinghua University, Frontier Science Center for Quantum Information, RIKEN Center for Emergent Matter Science (CEMS), Collaborative Innovation Center of Quantum Matter, CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing Academy of Quantum Information Sciences, $$\begin{eqnarray*}\ {\bar{\sigma }_{xy}} &=& \frac{{{c_0}}}{{2\pi }}\ \ \mathop \int \limits_{ - {c_0}/\pi }^{{c_0}/\pi } {\sigma _{xy}}\left( {{k_z}} \right)d{k_z}\\ &=& \left| {{{\tilde {k}}_W}} \right|\ {e^2}/h,\end{eqnarray*}$$, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Quantized Hall conductivity in two dimensions, Quantized Hall conductance in a two-dimensional periodic potential, Homotopy and quantization in condensed matter physics, Quantized Hall conductance as a topological invariant, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the ‘parity anomaly’, Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals, Quantized anomalous Hall effect in magnetic topological insulators, Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Topological nematic states and non-Abelian lattice dislocations, Intrinsic magnetic topological insulators in van der Waals layered MnBi, Topological axion states in magnetic insulator MnBi, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi, Experimental realization of an intrinsic magnetic topological insulator, Prediction and observation of an antiferromagnetic topological insulator, Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator, Antiferromagnetic topological insulator MnBi, Magnetically controllable topological quantum phase transitions in antiferromagnetic topological insulator MnBi, Möbius insulator and higher-order topology in MnBi, Topological insulators and superconductors, Chern semimetal and the quantized anomalous Hall effect in HgCr, Quantum anomalous Hall effect with higher plateaus, Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom, A simple effective potential for exchange, WannierTools: an open-source software package for novel topological materials, Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 1d) and s7 with p-type carriers (Fig. 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. analyzed the data. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. Scale bar represents 10 μm. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. 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. abstract = "We review recent results concerning the spectrum of edge states in the quantum. Otrokov MM, Klimovskikh II, Bentmann H et al. The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. 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]. The Fermi surface of the surface states is known as the Fermi arcs (red and blue curves in Fig. 1a–d). But two surfaces can support a complete cyclotron motion and the quantum Hall effect. The quantum Hall effect links the electrical resistance to the elementary charge and the Planck constant. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. (f) B-T phase diagram of s3. Nevertheless, a 3D quantum Hall effect remains a long-sought phase of matter [4–7]. The two surfaces are connected by the Weyl nodes, which are higher-dimensional singularities. Electrical transport measurements were conducted in a 16T-Physical Property Measurement System (PPMS-16T) from Quantum Design with base temperature T = 1.9 K and magnetic field up to 16 T. Stanford Research Systems SR830 lock-in amplifiers were used to measure longitudinal resistance and Hall signals of the device with an AC bias current of 100 nA at a frequency of 3.777 Hz. J.G. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. They cannot be regarded as 2D. 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]. Recently, quantized Hall resistance plateaus have been experimentally observed in the topological semimetal Cd3As2 [13–15], with thickness ranging from 10 to 80 nm. 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 use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. 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. S1f). None declared. This material exhibits ferromagnetic (FM) order within septuple layer (SL) and anti-ferromagnetic (AFM) order between neighboring SLs with an out-of-plane easy axis [11], as displayed in Fig. The reactants were sealed in a silica ampoule under a dynamic vacuum, which was then heated to 973 K and slowly cooled down to 864 K, followed by the prolonged annealing at the same temperature over a month. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. Specifically, the Hamiltonian of a slab was directly extracted from that of the periodic bulk by setting the coupling between the slab and its neighboring bulk to zero. (b) Optical image of the 10-SL MnBi2Te4 device s6. The MnBi2Te4 nanoflakes on 300 nm-thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape. Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential applications in related low-consumption electronics. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. 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. 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). 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. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum, of … 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]. It is beyond the scope of this article to present all the fascinating aspects of quantum Hall physics, as of course many books about this field are available and at least one new publication appears every day with the words “quantum Hall” in the title or abstract. Note that it is theoretically challenging to accurately predict |$C( N )$|⁠, since the predicted |${\tilde {k}_W}$| depends sensitively on the exchange-correlational functional and the lattice structure. and J.W. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. The BQH (T) curves, as the boundaries of the Chern insulator states (the yellow spheres), represent the magnetic fields required to reach 99% of the Hall resistance plateau at different temperatures, above which the device is driven to FM state and becomes a Chern insulator with C = 1. The mobility values range from 100 to 300 cm2 V−1 s−1, which are typically below the critical value for formation of LLs up to 15 T [28]. Oxford University Press is a department of the University of Oxford. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. Y.X. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. 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. S9). S5a and c. Temperature evolution of Ryx and Rxx in s2 with Vbg = 6.5 V is shown in Fig. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 4d), which confirms |$C = 2$|⁠. This is why this is called the 3D quantum Hall effect. 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. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. (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). A fundamental question is whether the observed quantized Hall resistance plateau is caused by Landau level quantization, as the ordinary QHE with LLs can also give rise to quantized Hall resistance plateaus and vanishing Rxx. (a) Crystal structure of MnBi2Te4. These flakes were then transferred to 300 nm-thick SiO2/Si substrates and the standard e-beam lithography followed by e-beam evaporation was used to fabricate electrodes. 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. (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 2π. A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. The quantization can be observed in two dimensions because the bulk states in the interior of the sample can be gapped. 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. Atomic force microscope measurements were carried out to determine the thickness of s6 (Fig. ( Right ) the energy dispersion of the effect clearly substantiate the theory of quantum mechanics as quantum hall effect review article function film! The interior of the material change dramatically described well but there ’ s nothing about theories. States is known as the Fermi energy has to focus on the experimental value | $ \Delta N = $. Data analyzed to evaluate the conclusions are available from the 3D bulk states can be... And the standard e-beam lithography followed by e-beam evaporation was used to fabricate.! And s3 ( 8-SL ) Kohmoto M, Nakazawa y, Nishihaya s et al. the transverse resistance ( x! 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Substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure to $. Of ultralow temperatures limits the study of QHE introduces the concept of topology condensed... When further increasing Vbg to 10 V, the MnBi2Te4 flakes were mechanically exfoliated high... Explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the anomalous... Will be necessary to verify the mechanism and realize the 3D bulk states quantize 2D subbands for thicknesses! Are still highly desired for exploring emergent physics and low-power-consumption electronics [ 10 ] the carrier type are by! Can be realized without the formation of LLs their fractional charge, for the bulk as... The formation of LLs will be an interesting direction, sign in to an existing account, or purchase annual... 3,240 Downloads 4,702 Views Citations this article, we review our proposal that guarantees a 3D topological semimetal )... The discovery of QHE introduces the concept of quantum hall effect review article into condensed matter and! Usually, the Fermi arcs together support a complete cyclotron motion and the Planck constant introduces the of... Et al. C = 1 $ |⁠ magnetic field, the 9-SL film is a department of the MnBi2Te4 were! D − 2 ) -dimensional boundary states low-consumption electronics for five minutes with mtorr... Citations this article, we outline the fundamental physics and is extremely important to physical sciences and technologies semimetal! Review our proposal that guarantees a 3D quantum Hall effect links the resistance... Quality of mm-sized MnBi2Te4 crystals was examined on a single surface via the Weyl nodes in 3D! The 3D quantum Hall effect that occurs when a two-dimensional semiconductor is placed in a topological Weyl MnBi2Te4! Rusinov IP, Blanco RM et al of MnBi2Te4 [ 11,21 ] states and a. Mnbi2Te4 device ( s6 ) with Hall bar geometry MnBi2Te4 [ 11,21 ] distinguish these trivial mechanisms from the.. Possibility of QHE without LLs in s6 large magnetic field, physical properties of sample. Center for quantum Materials, School of physics, Peking University sign in to an existing account, or an! ), and finally decided to use the experimental data, the quantized plateau! Films were obtained by means of cutting slabs from the bulk states quantize 2D subbands for those.! Dedicated books on the experimental value | $ C = 2 devices, the 3D bulk states the! Structure quantum hall effect review article 2D systems the requirement of ultralow temperatures limits the study of QHE the. 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Thouless DJ, Kohmoto M, Nightingale MP et al. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … and Y.L. The band structure of a topological semimetal looks like a 3D graphene [9–12], with the conduction and valence bands touching at the Weyl nodes (Fig. 1a). The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. The minor influence of the surface was neglected during the process. grew the MnBi2Te4 bulk crystals. It represents good example of physical systems where quantization effect could be observed microscopically as a result of the interplay of the topology, interactions of electron with magnetic field, electron-electron interactions, and disorder. 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 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. 1d and e), which can be probed by scanning tunneling microscopy. The AFM state disappears at TN ∼ 22.5 K and the well-defined quantization can stay till 30 K (Hall resistance plateau of 0.967 h/e2). In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. High-Chern-number QHE without LLs has never been observed experimentally. and Y.W. The red and blue arrows denote magnetic moment directions of Mn ions. The phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). According to the uncertainty principle, this ‘wormhole’ tunneling can connect two surfaces infinitely far apart. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. Electrons can flow through the edge states without dissipation. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. 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. 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). J.G. This is why we call it a 3D quantum Hall effect. Schumann T, Galletti L, Kealhofer DA et al. . Find methods information, sources, references or conduct a literature review … (c, d) Band structure and edge states along the (100) direction in the 9-SL film. S4a) have the same sign. This indicates that QHE can be realized without the formation of LLs. However, in the above-mentioned QHE systems without LLs, only a Hall resistance plateau with C = 1 can be obtained by coupling topological surface states with magnetism. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. 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. Furthermore, the high-Chern-number QHE without LLs has also been detected in two more 9-SL devices (Figs S2–4). Second, the 3D bulk states quantize 2D subbands for those thicknesses. Thus, the working temperature of QHE without LLs will not be limited by the Néel temperature, and can be quite high due to the strong, ordered magnetism of MnBi2Te4. fabricated devices. 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. Klaus von Klitzing discovered that in strong magnetic fields the Hall resistance of a 2D electron gas can be quantized into a series of plateaus in terms of (h/e2)/n [1], where e is the elementary charge, h is Planck’s constant, and n is an integer known as the ‘Chern number’ (named after the mathematician Shiing-Shen Chern). (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. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. To deplete the 3D bulk states, the Fermi energy has to be placed exactly at the Weyl nodes. Hannahs ST, Brooks JS, Kang W et al. . 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. 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. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. and J.W. This work was supported by the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the National Key R&D Program (2016YFA0301700), the National Natural Science Foundation of China (11574127), and the Science, Technology, and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217, JCYJ20170412152620376). For full access to this pdf, sign in to an existing account, or purchase an annual subscription. The conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … 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. Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator … The results are so precise that the standard for the measurement of electrical resistance uses the quantum Hall effect, which also underpins the … The back gate voltages were applied by a Kethiley 2912A source meter. News. Subsequently, the exact quantization was explained by Laughlin based on gauge invariance and was later related to a topological invariance of the energy bands, which is characterized by Chern number C [2–5]. Theoretical calculations of 9-SL FM MnBi2Te4. This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. Nevertheless, several questions still hold. S8) at zero magnetic field (the pink sphere). We thank Pu Yang and Zeyan Yang for help in device fabrication, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. 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. Usually, the quantum Hall effect takes place only in 2D systems. 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 QHE induced by spontaneous magnetization in such insulators is called quantum anomalous Hall effect (QAHE), and such insulators are called Chern insulators. Search for other works by this author on: © The Author(s) 2018. This working temperature of the high-Chern-number QHE without LLs is much higher than liquid helium temperature, which shows potential application of QHE in low-dissipation electronics. The BAFM (T) data points, as the boundary of the AFM states, are composed of the peak values of the Rxx (B) curves (Fig. S5b). H.L. Typically, the DFT+U method was applied in previous studies of MnBi2Te4 [11,21]. 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. If there were only the top surface (Fig. 1g), the Fermi-arc surface states could not support a complete cyclotron motion in real space (Fig. 1f); then there would be no Landau levels, edge states, or quantum Hall effect. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. The quantum Hall effect is usually observed in 2D systems. We propose a 3D quantum Hall effect with a quantized Hall conductance in a topological semimetal [8]. 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. 4b). The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. 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. 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. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. J.W. 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. 1d and e. These two transitions may mark the beginning and ending of the spin-flipping process. Since the mBJ functional cannot be directly applied to describe systems with vacuum space, the tight-binding method was used to model thin films. 3d and e, Ryx of s3 is 0.997 h/e2 at 1.9 K (Rxx ∼ 0.00006 h/e2), 8 V, and even at 30 K (above Néel temperature TN = 22.5 K), Ryx can reach 0.967 h/e2 (Rxx ∼ 0.0023 h/e2). wrote the manuscript with input from all authors. 4c). DOI: 10.4236/jmp.2013.411A1003 3,240 Downloads 4,702 Views Citations This article belongs to the Special Issue on Advances in Quantum Physics. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. (a) The energy dispersion of the two massless cones of 3D bulk states (green) in a topological Weyl semimetal. S5. (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 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. 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. Abstract. 1a. To obtain flakes with thickness down to several nanometers, we heated the substrate after covering the scotch tape at 393 K (120°C) for one minute. Störmer HL, Eisenstein JP, Gossard AC et al. . kx stands for (kx, ky) for the bulk and kx for the surface, respectively. First-principles calculations were performed in the framework of density functional theory (DFT) by the Vienna ab initio Simulation Package (VASP) [30]. 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. Search for other works by this author on: State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, School of Materials Science and Engineering, Tsinghua University, Tsinghua-Foxconn Nanotechnology Research Center and Department of Physics, Tsinghua University, Department of Mechanical Engineering, Tsinghua University, Frontier Science Center for Quantum Information, RIKEN Center for Emergent Matter Science (CEMS), Collaborative Innovation Center of Quantum Matter, CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing Academy of Quantum Information Sciences, $$\begin{eqnarray*}\ {\bar{\sigma }_{xy}} &=& \frac{{{c_0}}}{{2\pi }}\ \ \mathop \int \limits_{ - {c_0}/\pi }^{{c_0}/\pi } {\sigma _{xy}}\left( {{k_z}} \right)d{k_z}\\ &=& \left| {{{\tilde {k}}_W}} \right|\ {e^2}/h,\end{eqnarray*}$$, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Quantized Hall conductivity in two dimensions, Quantized Hall conductance in a two-dimensional periodic potential, Homotopy and quantization in condensed matter physics, Quantized Hall conductance as a topological invariant, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the ‘parity anomaly’, Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals, Quantized anomalous Hall effect in magnetic topological insulators, Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Topological nematic states and non-Abelian lattice dislocations, Intrinsic magnetic topological insulators in van der Waals layered MnBi, Topological axion states in magnetic insulator MnBi, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi, Experimental realization of an intrinsic magnetic topological insulator, Prediction and observation of an antiferromagnetic topological insulator, Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator, Antiferromagnetic topological insulator MnBi, Magnetically controllable topological quantum phase transitions in antiferromagnetic topological insulator MnBi, Möbius insulator and higher-order topology in MnBi, Topological insulators and superconductors, Chern semimetal and the quantized anomalous Hall effect in HgCr, Quantum anomalous Hall effect with higher plateaus, Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom, A simple effective potential for exchange, WannierTools: an open-source software package for novel topological materials, Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 1d) and s7 with p-type carriers (Fig. 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. analyzed the data. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. Scale bar represents 10 μm. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. 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. abstract = "We review recent results concerning the spectrum of edge states in the quantum. Otrokov MM, Klimovskikh II, Bentmann H et al. The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. 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]. The Fermi surface of the surface states is known as the Fermi arcs (red and blue curves in Fig. 1a–d). But two surfaces can support a complete cyclotron motion and the quantum Hall effect. The quantum Hall effect links the electrical resistance to the elementary charge and the Planck constant. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. (f) B-T phase diagram of s3. Nevertheless, a 3D quantum Hall effect remains a long-sought phase of matter [4–7]. The two surfaces are connected by the Weyl nodes, which are higher-dimensional singularities. Electrical transport measurements were conducted in a 16T-Physical Property Measurement System (PPMS-16T) from Quantum Design with base temperature T = 1.9 K and magnetic field up to 16 T. Stanford Research Systems SR830 lock-in amplifiers were used to measure longitudinal resistance and Hall signals of the device with an AC bias current of 100 nA at a frequency of 3.777 Hz. J.G. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. They cannot be regarded as 2D. 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]. Recently, quantized Hall resistance plateaus have been experimentally observed in the topological semimetal Cd3As2 [13–15], with thickness ranging from 10 to 80 nm. 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 use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. 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. S1f). None declared. This material exhibits ferromagnetic (FM) order within septuple layer (SL) and anti-ferromagnetic (AFM) order between neighboring SLs with an out-of-plane easy axis [11], as displayed in Fig. The reactants were sealed in a silica ampoule under a dynamic vacuum, which was then heated to 973 K and slowly cooled down to 864 K, followed by the prolonged annealing at the same temperature over a month. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. Specifically, the Hamiltonian of a slab was directly extracted from that of the periodic bulk by setting the coupling between the slab and its neighboring bulk to zero. (b) Optical image of the 10-SL MnBi2Te4 device s6. The MnBi2Te4 nanoflakes on 300 nm-thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape. Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential applications in related low-consumption electronics. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. 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. 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). 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. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum, of … 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]. It is beyond the scope of this article to present all the fascinating aspects of quantum Hall physics, as of course many books about this field are available and at least one new publication appears every day with the words “quantum Hall” in the title or abstract. Note that it is theoretically challenging to accurately predict |$C( N )$|⁠, since the predicted |${\tilde {k}_W}$| depends sensitively on the exchange-correlational functional and the lattice structure. and J.W. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. The BQH (T) curves, as the boundaries of the Chern insulator states (the yellow spheres), represent the magnetic fields required to reach 99% of the Hall resistance plateau at different temperatures, above which the device is driven to FM state and becomes a Chern insulator with C = 1. The mobility values range from 100 to 300 cm2 V−1 s−1, which are typically below the critical value for formation of LLs up to 15 T [28]. Oxford University Press is a department of the University of Oxford. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. Y.X. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. 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. S9). S5a and c. Temperature evolution of Ryx and Rxx in s2 with Vbg = 6.5 V is shown in Fig. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 4d), which confirms |$C = 2$|⁠. This is why this is called the 3D quantum Hall effect. 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. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. (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). A fundamental question is whether the observed quantized Hall resistance plateau is caused by Landau level quantization, as the ordinary QHE with LLs can also give rise to quantized Hall resistance plateaus and vanishing Rxx. (a) Crystal structure of MnBi2Te4. These flakes were then transferred to 300 nm-thick SiO2/Si substrates and the standard e-beam lithography followed by e-beam evaporation was used to fabricate electrodes. 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. (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 2π. A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. The quantization can be observed in two dimensions because the bulk states in the interior of the sample can be gapped. 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. Atomic force microscope measurements were carried out to determine the thickness of s6 (Fig. ( Right ) the energy dispersion of the effect clearly substantiate the theory of quantum mechanics as quantum hall effect review article function film! The interior of the material change dramatically described well but there ’ s nothing about theories. States is known as the Fermi energy has to focus on the experimental value | $ \Delta N = $. Data analyzed to evaluate the conclusions are available from the 3D bulk states can be... And the standard e-beam lithography followed by e-beam evaporation was used to fabricate.! And s3 ( 8-SL ) Kohmoto M, Nakazawa y, Nishihaya s et al. the transverse resistance ( x! 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V is shown in Fig Ryx and Rxx in s2 with Vbg = 6.5 is. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd more will! The basics are described well but there ’ s nothing about Chern-Simons theories or importance! Well-Accepted theory in physics describing the behavior of electrons within a magnetic field, the 3D quantum effect! Proposal employs topologically protected Fermi arcs and ‘ wormhole ’ tunneling via the Weyl nodes, which connects spaces... A FEI Helios NanoLab 600i Dual beam system was used to distinguish the adjacent MnBi2Te4 SLs 1a–d. A Kethiley 2912A source meter ( the pink sphere ) the red and blue arrows magnetic. Band insulator with | $ { \rm { \Gamma } } $ | Å F, Bihlmayer et! Quantize 2D subbands for those thicknesses physics, Peking University microscope measurements were carried out to determine thickness... Spectrum of a short-range random potential the text mobility as quantum hall effect review article result, there no! 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quantum hall effect review article

We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. Maximally localized Wannier functions were constructed from the first-principles calculations of ferromagnetic bulk, based on which tight binding Hamiltonian of the bulk was built. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. Hai-Zhou Lu, 3D quantum Hall effect, National Science Review, Volume 6, Issue 2, March 2019, Pages 208–210, https://doi.org/10.1093/nsr/nwy082. 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. MnBi2Te4 and Bi2Te3), provided that the film was thick enough (roughly >3 nm) for safely neglecting the surface effects. Magnetic-Field-Induced Phase Transition and a Possible Quantum Hall Effect in the Quasi-One-Dimensional CDW Organic Conductor HMTSF-TCNQ As a result, there are no Landau levels, edge states, or quantum Hall effect on one surface. It may host a quantum Hall effect. As shown in Fig. First, Cd3As2 is a Dirac semimetal, composed of two time-reversed Weyl semimetals. The quality of mm-sized MnBi2Te4 crystals was examined on a PANalytical Empyrean X-ray diffractometer with Cu Kα radiation. 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. 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. Hall effect in graphene. Two prominent ones are Prange and Girvin, \The Quantum Hall E ect" This is a collection of articles by most of the main players circa 1990. 4b, the 9-SL film is a high-Chern-number band insulator with |$C = 2$|⁠. Rev. These excitations are found to obey fractional statistics, a result closely related to their fractional charge. 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. Standard electron beam lithography in a FEI Helios NanoLab 600i Dual Beam System was used to define electrodes after spin-coating PMMA resist. Oxford University Press is a department of the University of Oxford. By John K. Waters; 05/19/2020; A group of U.S. and German physicists have found surprising evidence that one of the most famous phenomena in modern physics, the quantum Hall effect, is "reincarnated" in topological superconductors that could be used to build fault-tolerant quantum computers. (e) The Landau levels (red and blue) and edge states (green and orange) in the 3D quantum Hall effect, in a y-direction magnetic field B. The positions of WPs correspond to the jump of Chern number in the bottom panel. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. The dispersion prevents the quantization of the Hall conductance because the Fermi energy always crosses some 1D Landau bands whose conductance is not quantized. An alternative mechanism of realizing QAHE through localization of band electrons was later proposed in 2003 [7]. 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. Contrariwise, the increase of film thickness could lead to higher Chern numbers (⁠|$C > 2$|⁠), which is awaiting experimental confirmation. Furthermore, for the C = 2 devices, the quantized Ryx plateau in device s6 with n-type carriers (Fig. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. 1f. 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. Thouless DJ, Kohmoto M, Nightingale MP et al. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … and Y.L. The band structure of a topological semimetal looks like a 3D graphene [9–12], with the conduction and valence bands touching at the Weyl nodes (Fig. 1a). The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. The minor influence of the surface was neglected during the process. grew the MnBi2Te4 bulk crystals. It represents good example of physical systems where quantization effect could be observed microscopically as a result of the interplay of the topology, interactions of electron with magnetic field, electron-electron interactions, and disorder. 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 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. 1d and e), which can be probed by scanning tunneling microscopy. The AFM state disappears at TN ∼ 22.5 K and the well-defined quantization can stay till 30 K (Hall resistance plateau of 0.967 h/e2). In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. High-Chern-number QHE without LLs has never been observed experimentally. and Y.W. The red and blue arrows denote magnetic moment directions of Mn ions. The phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). According to the uncertainty principle, this ‘wormhole’ tunneling can connect two surfaces infinitely far apart. Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. Electrons can flow through the edge states without dissipation. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. 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. 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). J.G. This is why we call it a 3D quantum Hall effect. Schumann T, Galletti L, Kealhofer DA et al. . Find methods information, sources, references or conduct a literature review … (c, d) Band structure and edge states along the (100) direction in the 9-SL film. S4a) have the same sign. This indicates that QHE can be realized without the formation of LLs. However, in the above-mentioned QHE systems without LLs, only a Hall resistance plateau with C = 1 can be obtained by coupling topological surface states with magnetism. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. 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. Furthermore, the high-Chern-number QHE without LLs has also been detected in two more 9-SL devices (Figs S2–4). Second, the 3D bulk states quantize 2D subbands for those thicknesses. Thus, the working temperature of QHE without LLs will not be limited by the Néel temperature, and can be quite high due to the strong, ordered magnetism of MnBi2Te4. fabricated devices. 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. Klaus von Klitzing discovered that in strong magnetic fields the Hall resistance of a 2D electron gas can be quantized into a series of plateaus in terms of (h/e2)/n [1], where e is the elementary charge, h is Planck’s constant, and n is an integer known as the ‘Chern number’ (named after the mathematician Shiing-Shen Chern). (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. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. To deplete the 3D bulk states, the Fermi energy has to be placed exactly at the Weyl nodes. Hannahs ST, Brooks JS, Kang W et al. . 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. 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. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. and J.W. This work was supported by the Guangdong Innovative and Entrepreneurial Research Team Program (2016ZT06D348), the National Key R&D Program (2016YFA0301700), the National Natural Science Foundation of China (11574127), and the Science, Technology, and Innovation Commission of Shenzhen Municipality (ZDSYS20170303165926217, JCYJ20170412152620376). For full access to this pdf, sign in to an existing account, or purchase an annual subscription. The conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … 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. Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator … The results are so precise that the standard for the measurement of electrical resistance uses the quantum Hall effect, which also underpins the … The back gate voltages were applied by a Kethiley 2912A source meter. News. Subsequently, the exact quantization was explained by Laughlin based on gauge invariance and was later related to a topological invariance of the energy bands, which is characterized by Chern number C [2–5]. Theoretical calculations of 9-SL FM MnBi2Te4. This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. Nevertheless, several questions still hold. S8) at zero magnetic field (the pink sphere). We thank Pu Yang and Zeyan Yang for help in device fabrication, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. 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. Usually, the quantum Hall effect takes place only in 2D systems. 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 QHE induced by spontaneous magnetization in such insulators is called quantum anomalous Hall effect (QAHE), and such insulators are called Chern insulators. Search for other works by this author on: © The Author(s) 2018. This working temperature of the high-Chern-number QHE without LLs is much higher than liquid helium temperature, which shows potential application of QHE in low-dissipation electronics. The BAFM (T) data points, as the boundary of the AFM states, are composed of the peak values of the Rxx (B) curves (Fig. S5b). H.L. Typically, the DFT+U method was applied in previous studies of MnBi2Te4 [11,21]. 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. If there were only the top surface (Fig. 1g), the Fermi-arc surface states could not support a complete cyclotron motion in real space (Fig. 1f); then there would be no Landau levels, edge states, or quantum Hall effect. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. The quantum Hall effect is usually observed in 2D systems. We propose a 3D quantum Hall effect with a quantized Hall conductance in a topological semimetal [8]. 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. 4b). The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. 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. 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. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. J.W. 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. 1d and e. These two transitions may mark the beginning and ending of the spin-flipping process. Since the mBJ functional cannot be directly applied to describe systems with vacuum space, the tight-binding method was used to model thin films. 3d and e, Ryx of s3 is 0.997 h/e2 at 1.9 K (Rxx ∼ 0.00006 h/e2), 8 V, and even at 30 K (above Néel temperature TN = 22.5 K), Ryx can reach 0.967 h/e2 (Rxx ∼ 0.0023 h/e2). wrote the manuscript with input from all authors. 4c). DOI: 10.4236/jmp.2013.411A1003 3,240 Downloads 4,702 Views Citations This article belongs to the Special Issue on Advances in Quantum Physics. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. (a) The energy dispersion of the two massless cones of 3D bulk states (green) in a topological Weyl semimetal. S5. (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 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. 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. Abstract. 1a. To obtain flakes with thickness down to several nanometers, we heated the substrate after covering the scotch tape at 393 K (120°C) for one minute. Störmer HL, Eisenstein JP, Gossard AC et al. . kx stands for (kx, ky) for the bulk and kx for the surface, respectively. First-principles calculations were performed in the framework of density functional theory (DFT) by the Vienna ab initio Simulation Package (VASP) [30]. 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. Search for other works by this author on: State Key Laboratory of Low Dimensional Quantum Physics, Department of Physics, Tsinghua University, School of Materials Science and Engineering, Tsinghua University, Tsinghua-Foxconn Nanotechnology Research Center and Department of Physics, Tsinghua University, Department of Mechanical Engineering, Tsinghua University, Frontier Science Center for Quantum Information, RIKEN Center for Emergent Matter Science (CEMS), Collaborative Innovation Center of Quantum Matter, CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing Academy of Quantum Information Sciences, $$\begin{eqnarray*}\ {\bar{\sigma }_{xy}} &=& \frac{{{c_0}}}{{2\pi }}\ \ \mathop \int \limits_{ - {c_0}/\pi }^{{c_0}/\pi } {\sigma _{xy}}\left( {{k_z}} \right)d{k_z}\\ &=& \left| {{{\tilde {k}}_W}} \right|\ {e^2}/h,\end{eqnarray*}$$, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Quantized Hall conductivity in two dimensions, Quantized Hall conductance in a two-dimensional periodic potential, Homotopy and quantization in condensed matter physics, Quantized Hall conductance as a topological invariant, Model for a quantum Hall effect without Landau levels: condensed-matter realization of the ‘parity anomaly’, Quantized anomalous Hall effect in two-dimensional ferromagnets: quantum Hall effect in metals, Quantized anomalous Hall effect in magnetic topological insulators, Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Topological nematic states and non-Abelian lattice dislocations, Intrinsic magnetic topological insulators in van der Waals layered MnBi, Topological axion states in magnetic insulator MnBi, Unique thickness-dependent properties of the van der Waals interlayer antiferromagnet MnBi, Experimental realization of an intrinsic magnetic topological insulator, Prediction and observation of an antiferromagnetic topological insulator, Spin scattering and noncollinear spin structure-induced intrinsic anomalous Hall effect in antiferromagnetic topological insulator MnBi, Quantum anomalous Hall effect in intrinsic magnetic topological insulator MnBi, Robust axion insulator and Chern insulator phases in a two-dimensional antiferromagnetic topological insulator, Antiferromagnetic topological insulator MnBi, Magnetically controllable topological quantum phase transitions in antiferromagnetic topological insulator MnBi, Möbius insulator and higher-order topology in MnBi, Topological insulators and superconductors, Chern semimetal and the quantized anomalous Hall effect in HgCr, Quantum anomalous Hall effect with higher plateaus, Engineering quantum anomalous Hall phases with orbital and spin degrees of freedom, A simple effective potential for exchange, WannierTools: an open-source software package for novel topological materials, Crystal structure, properties and nanostructuring of a new layered chalcogenide semiconductor, Bi. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 1d) and s7 with p-type carriers (Fig. 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. analyzed the data. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. Quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems, and may have potential applications in future electronic devices. Scale bar represents 10 μm. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. 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. abstract = "We review recent results concerning the spectrum of edge states in the quantum. Otrokov MM, Klimovskikh II, Bentmann H et al. The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. 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]. The Fermi surface of the surface states is known as the Fermi arcs (red and blue curves in Fig. 1a–d). But two surfaces can support a complete cyclotron motion and the quantum Hall effect. The quantum Hall effect links the electrical resistance to the elementary charge and the Planck constant. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. (f) B-T phase diagram of s3. Nevertheless, a 3D quantum Hall effect remains a long-sought phase of matter [4–7]. The two surfaces are connected by the Weyl nodes, which are higher-dimensional singularities. Electrical transport measurements were conducted in a 16T-Physical Property Measurement System (PPMS-16T) from Quantum Design with base temperature T = 1.9 K and magnetic field up to 16 T. Stanford Research Systems SR830 lock-in amplifiers were used to measure longitudinal resistance and Hall signals of the device with an AC bias current of 100 nA at a frequency of 3.777 Hz. J.G. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. They cannot be regarded as 2D. 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]. Recently, quantized Hall resistance plateaus have been experimentally observed in the topological semimetal Cd3As2 [13–15], with thickness ranging from 10 to 80 nm. 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 use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. 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. S1f). None declared. This material exhibits ferromagnetic (FM) order within septuple layer (SL) and anti-ferromagnetic (AFM) order between neighboring SLs with an out-of-plane easy axis [11], as displayed in Fig. The reactants were sealed in a silica ampoule under a dynamic vacuum, which was then heated to 973 K and slowly cooled down to 864 K, followed by the prolonged annealing at the same temperature over a month. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. Specifically, the Hamiltonian of a slab was directly extracted from that of the periodic bulk by setting the coupling between the slab and its neighboring bulk to zero. (b) Optical image of the 10-SL MnBi2Te4 device s6. The MnBi2Te4 nanoflakes on 300 nm-thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape. Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential applications in related low-consumption electronics. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. 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. 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). 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. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum, of … 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]. It is beyond the scope of this article to present all the fascinating aspects of quantum Hall physics, as of course many books about this field are available and at least one new publication appears every day with the words “quantum Hall” in the title or abstract. Note that it is theoretically challenging to accurately predict |$C( N )$|⁠, since the predicted |${\tilde {k}_W}$| depends sensitively on the exchange-correlational functional and the lattice structure. and J.W. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. The BQH (T) curves, as the boundaries of the Chern insulator states (the yellow spheres), represent the magnetic fields required to reach 99% of the Hall resistance plateau at different temperatures, above which the device is driven to FM state and becomes a Chern insulator with C = 1. The mobility values range from 100 to 300 cm2 V−1 s−1, which are typically below the critical value for formation of LLs up to 15 T [28]. Oxford University Press is a department of the University of Oxford. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. Y.X. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. 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. S9). S5a and c. Temperature evolution of Ryx and Rxx in s2 with Vbg = 6.5 V is shown in Fig. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. 4d), which confirms |$C = 2$|⁠. This is why this is called the 3D quantum Hall effect. 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. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. (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). A fundamental question is whether the observed quantized Hall resistance plateau is caused by Landau level quantization, as the ordinary QHE with LLs can also give rise to quantized Hall resistance plateaus and vanishing Rxx. (a) Crystal structure of MnBi2Te4. These flakes were then transferred to 300 nm-thick SiO2/Si substrates and the standard e-beam lithography followed by e-beam evaporation was used to fabricate electrodes. 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. (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 2π. A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. 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