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. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. The temperature dependence of longitudinal resistance Rxx is shown in Fig. and Y.W. The discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. The QHE induced by spontaneous magnetization in such insulators is called quantum anomalous Hall effect (QAHE), and such insulators are called Chern insulators. Based on the mBJ functional [29], we systematically tested the influence of lattice parameter |${c_0}$| on band structure and |$C( N )$| (Fig. Quantum Hall Effect 'Reincarnated' in 3D Topological Superconductors. 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. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. Since the position of Weyl points in momentum space and the topological Chern number of thin films depend sensitively on the out-of-lattice constant c = 3c0, structures with different c0 ranging from theoretical (⁠|${c_0} = 13.53$| Å) [11] to experimental (⁠|${c_0} = 13.6$| Å) [32] values were systematically studied and compared (Fig. 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 conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … 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]. (a, b) Ryx and Rxx as a function of magnetic field at different temperatures from 2 K to 15 K. The height of Hall resistance plateau can reach 0.97 h/2e2 at 13 K. We further study the 7-SL and 8-SL MnBi2Te4 devices (s2 and s3) and the results are displayed in Fig. S4a) have the same sign. The positions of WPs correspond to the jump of Chern number in the bottom panel. These two issues may explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the experiments. J.G., Y.L., T.L. The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. The black spots stand for the Weyl nodes. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. Störmer HL, Eisenstein JP, Gossard AC et al. . The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. (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 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. 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. 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. Nevertheless, several questions still hold. 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. News. Zhang H, Freimuth F, Bihlmayer G et al. Find methods information, sources, references or conduct a literature review … Second, the 3D bulk states quantize 2D subbands for those thicknesses. The use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. Figure 3c and f displays the color plot of Ryx in s2 and s3 as a function of the temperature and magnetic field at Vbg = 6.5 V and 8 V, respectively. © The Author(s) 2020. kx stands for (kx, ky) for the bulk and kx for the surface, respectively. (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). When further increasing Vbg to 10 V, the quantized Hall resistance plateaus remain robust as shown in Fig. In this work, the MnBi2Te4 flakes were mechanically exfoliated from high-quality MnBi2Te4 single crystals. 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. 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. 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. The red and blue arrows denote magnetic moment directions of Mn ions. The high-temperature QHE without LLs is also observed in the 8-SL device s3. 1a. 4b). Based on the experimental data, the B-T phase diagram can be summarized. To further exclude the possibility of QHE with LLs, we performed controlled measurements by changing the carrier type. By reducing the film thickness to 7-SL, the Chern number decreases to |$C = 1$|⁠, as found experimentally. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. In contrast, a magnetic field quantizes the energy spectrum of a 3D electron gas into 1D Landau bands that disperse along the direction of the magnetic field. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. The quantum Hall effect (QHE) with quantized Hall resistance of h/νe2 started the research on topological quantum states and laid the foundation of topology in physics. S8) at zero magnetic field (the pink sphere). carried out theoretical calculations. Rev. Then, metal electrodes (Ti/Au or Cr/Au, 65/180 nm) were deposited in a LJUHV E-400 L E-Beam Evaporator after Ar plasma cleaning. The quantum Hall effect links the electrical resistance to the elementary charge and the Planck constant. (a) The illustration of band structure along the kz direction and the kz-dependent Chern number in the FM bulk phase of MnBi2Te4, which is a magnetic Weyl semimetal. Figure 1g shows the schematic FM order and electronic structure of the C = 2 Chern insulator state with two chiral edge states across the band gap. 4b, the 9-SL film is a high-Chern-number band insulator with |$C = 2$|⁠. (b) The Chern number as a function of film thickness. At a single surface, there is a complete 2D electron gas, formed by two time-reversed half-2D electron gases of the Fermi-arc surface states. Possible signatures of the 3D quantum Hall effect have been observed … The 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. Thouless DJ, Kohmoto M, Nightingale MP et al. The basics are described well but there’s nothing about Chern-Simons theories or the importance of the edge modes. Driven by the y-direction magnetic field, an electron performs half of a cyclotron motion on the top Fermi arc, then tunnels via a Weyl node to the bottom Fermi arc to complete the cyclotron motion. The quantum Hall effect (QHE) with quantized Hall resistance plateaus of height h/νe2 was first observed in two-dimensional (2D) electron systems in 1980 [1]. Gate-dependent transport properties of the 10-SL MnBi2Te4 device s6. However, when MnBi2Te4 is driven from AFM to FM states by external magnetic field, physical properties of the material change dramatically. With the temperature further increasing to 15 K, the value of the Hall resistance plateau reduces to 0.964 h/2e2 and Rxx increases to 0.032 h/2e2. The Fermi-arc surface states form a unique 2D electron gas, half from the top surface and half from the bottom surface (Fig. 1c and d). 3 and Fig. Schumann T, Galletti L, Kealhofer DA et al. . The edge-state calculation reveals that there exist two chiral gapless edge channels within the gap (Fig. Generally, |${\sigma _{xy}}$| of thin films would grow with film thickness, as its ideal bulk contribution is |$N| {{{\tilde {k}}_W}} |{e^2}/h$|⁠. The emergence of topological insulators (TIs) in which strong spin-orbit coupling (SOC) gives rise to topological band structures provides a new system for the investigation of QHE without strong external magnetic field. In this article, we review the theoretical foundations and experimental discovery of the quantum spin Hall effect. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. Nevertheless, a 3D quantum Hall effect remains a long-sought phase of matter [4–7]. As shown in Fig. J.G. Scale bar represents 10 μm. The phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. Contrariwise, the increase of film thickness could lead to higher Chern numbers (⁠|$C > 2$|⁠), which is awaiting experimental confirmation. Here we report the first experimental discovery of the high-Chern-number QHE without LLs above 10 K and C = 1 QHE without LLs above the Néel temperature (TN) in MnBi2Te4 devices. An alternative mechanism of realizing QAHE through localization of band electrons was later proposed in 2003 [7]. We thank Pu Yang and Zeyan Yang for help in device fabrication, and Jiawei Luo and Jiawei Zhang for helpful discussion in transport measurements. To obtain flakes with thickness down to several nanometers, we heated the substrate after covering the scotch tape at 393 K (120°C) for one minute. The reactants were sealed in a silica ampoule under a dynamic vacuum, which was then heated to 973 K and slowly cooled down to 864 K, followed by the prolonged annealing at the same temperature over a month. They cannot be regarded as 2D. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, Input associativity underlies fear memory renewal, Confined nanospace for enhanced photocatalysis, Role of cell cycle progression on analyzing telomerase in cancer cells based on aggregation-induced emission luminogens, Tracking the origin of ultralow velocity zones at the base of Earth's mantle, http://creativecommons.org/licenses/by/4.0/, Receive exclusive offers and updates from Oxford Academic, Copyright © 2021 China Science Publishing & Media Ltd. (Science Press). Abstract. S9), and finally decided to use the experimental value |${c_0} = 13.6$| Å. The BAFM (T) data points, as the boundary of the AFM states, are composed of the peak values of the Rxx (B) curves (Fig. The MnBi2Te4 nanoflakes on 300 nm-thick SiO2/Si substrate were mechanically exfoliated from high quality single crystals using scotch tape. Magnetic-Field-Induced Phase Transition and a Possible Quantum Hall Effect in the Quasi-One-Dimensional CDW Organic Conductor HMTSF-TCNQ (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). 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. S5a and c. Temperature evolution of Ryx and Rxx in s2 with Vbg = 6.5 V is shown in Fig. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. As a result, there are no Landau levels, edge states, or quantum Hall effect on one surface. As shown in Fig. (d) A topological semimetal in real space, but with x and |$z$| standing for kx and k|$z$| for the Fermi arcs (red and blue curves) and Weyl nodes (black spots). 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. S5b). 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]. 3b and e) at various temperatures (the cyan spheres) and the peak value of the Rxx (T) curve (Fig. 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). 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 discrepancy is possibly caused by the surface/interface effects that are not theoretically considered. abstract = "We review recent results concerning the spectrum of edge states in the quantum. 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