Because of the topological constraint, the Fermi arc at a single surface has an open Fermi surface, which cannot host the quantum Hall effect. The use of the quantum Hall effect was reviewed for the precise measurement of electrical resistance. As a result, there are no Landau levels, edge states, or quantum Hall effect on one surface. There may also be a trivial quantum Hall effect on a single surface. and J.W. 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. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number | C | = 1, which has been experimentally observed at relatively low temperatures. 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. In this work, the MnBi2Te4 flakes were mechanically exfoliated from high-quality MnBi2Te4 single crystals. But two surfaces can support a complete cyclotron motion and the quantum Hall effect. The discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. 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). An alternative mechanism of realizing QAHE through localization of band electrons was later proposed in 2003 [7]. 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. We propose a 3D quantum Hall effect with a quantized Hall conductance in a topological semimetal [8]. This indicates that QHE can be realized without the formation of LLs. Quantum Hall Effect 'Reincarnated' in 3D Topological Superconductors. 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. S5a and c. Temperature evolution of Ryx and Rxx in s2 with Vbg = 6.5 V is shown in Fig. 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. In this paper we present the concept of anyons, we explain why the observation of the fractional quantum Hall effect almost forces the notion of anyons upon us, and we review several possible ways for a direct observation of the physics of anyons. 4b). Contrariwise, the increase of film thickness could lead to higher Chern numbers (⁠|$C > 2$|⁠), which is awaiting experimental confirmation. With further application of a perpendicular magnetic field, the sample is supposed to enter the perfectly aligned FM state [19]. The two surfaces are connected by the Weyl nodes, which are higher-dimensional singularities. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. 4c). Moreover, since the Chern insulator phase appears in the FM state, the weak inter-SL anti-ferromagnetic exchange coupling is irrelevant to the topological physics. 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. The proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. 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. In the absence of a magnetic field, MnBi2Te4 bulk is an AFM TI, whose side surfaces are gapless and (111) surfaces are intrinsically gapped by exchange interactions [11,12,21]. (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). 3 and Fig. 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. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics: the quantum Hall effect. Rev. 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. The gapped surface states are characterized by a quantized Berry phase of |$\pi $| and can display the novel half-quantum Hall effect [23,24]. The quantum Hall effect (QHE) with quantized Hall resistance of h/νe 2 started the research on topological quantum states and laid the foundation of topology in physics. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. The search for topological states of matter that do not require magnetic fields for their observation led to the theoretical prediction in 2006 and experimental observation in 2007 of the so-called quantum spin Hall effect in HgTe quantum wells, a new topological state of quantum matter. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. MnBi2Te4 is a layered material which can be viewed as a layer of Bi2Te3 TI intercalated with an additional Mn-Te layer [11–20]. Generally, |${\sigma _{xy}}$| of thin films would grow with film thickness, as its ideal bulk contribution is |$N| {{{\tilde {k}}_W}} |{e^2}/h$|⁠. 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. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. Published by Oxford University Press on behalf of China Science Publishing & Media Ltd. Usually, the quantum Hall effect takes place only in 2D systems. H.L. However, when MnBi2Te4 is driven from AFM to FM states by external magnetic field, physical properties of the material change dramatically. Zhang H, Freimuth F, Bihlmayer G et al. 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 … The grey and green colors are used to distinguish the adjacent MnBi2Te4 SLs. Besides, the requirement of ultralow temperatures limits the study of QHE without LLs. For emerging physics and low-power-consumption electronics, the key issues are how to increase the working temperature and realize high Chern numbers (C > 1). 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]. The Fermi surface of the surface states is known as the Fermi arcs (red and blue curves in Fig. 1a–d). The tight binding method for thin films was systematically tested and proved to be able to well reproduce DFT results of variant exchange-correlation functionals for different van der Waals materials (e.g. Search for other works by this author on: © The Author(s) 2018. Furthermore, for the C = 2 devices, the quantized Ryx plateau in device s6 with n-type carriers (Fig. Second, the 3D bulk states quantize 2D subbands for those thicknesses. S9). J.G., Y.L., J.L., Y.X. International Center for Quantum Materials, School of Physics, Peking University. The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. As shown in Fig. Fortunately, the top and bottom surfaces can form a complete 2D electron gas, with a closed Fermi surface connected by the Weyl nodes. Theoretical calculations of 9-SL FM MnBi2Te4. The 1D edge states in this 3D quantum Hall effect show an example of (d − 2)-dimensional boundary states. 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. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. 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. 4b, the 9-SL film is a high-Chern-number band insulator with |$C = 2$|⁠. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. Atomic force microscope measurements were carried out to determine the thickness of s6 (Fig. A review article about my career as a solid-state physicist has to focus on the quantum Hall effect (QHE). Theoretical proposals based on the intrinsic band structure of 2D systems open up new opportunities. analyzed the data. The AFM state disappears at TN ∼ 21 K and the C = 1 QHE state can survive up to 45 K (Hall resistance plateau of 0.904 h/e2), much higher than TN. 4d), which confirms |$C = 2$|⁠. In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. When further increasing Vbg to 10 V, the quantized Hall resistance plateaus remain robust as shown in Fig. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. In particular, special attention is paid to the derivation of the conditions under which gapless edge states exist in the spectrum of graphene with "zigzag" and "armchair" edges. These excitations are found to obey fractional statistics, a result closely related to their fractional charge. Otrokov MM, Klimovskikh II, Bentmann H et al. The substrates were pre-cleaned in oxygen plasma for five minutes with ∼60 mtorr pressure. The red and blue arrows denote magnetic moment directions of Mn ions. The quantum Hall effect is a well-accepted theory in physics describing the behavior of electrons within a magnetic field at extremely low temperatures. (f) Rxx and Ryx as a function of Vbg at 2 K and −15 T. (g) The schematic FM order and electronic structure of the C = 2 Chern insulator state with two chiral edge states across the band gap. performed transport measurements. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), China, Shenzhen Key Laboratory of Quantum Science and Engineering, China. Hannahs ST, Brooks JS, Kang W et al. . A prefactor of the activated dissipative conductivity in the quantum Hall regime is studied in the case of a short-range random potential. The black and red traces represent magnetic field sweeping to the positive and negative directions, respectively. This is why this is called the 3D quantum Hall effect. 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). The temperature dependence of longitudinal resistance Rxx is shown in Fig. (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. 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. 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]. Hall effect in graphene. A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. and J.W. Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. To further exclude the possibility of QHE with LLs, we performed controlled measurements by changing the carrier type. Nevertheless, a 3D quantum Hall effect remains a long-sought phase of matter [4–7]. These two issues may explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the experiments. conceived and supervised the experiments. S9). Furthermore, the high-Chern-number QHE without LLs has also been detected in two more 9-SL devices (Figs S2–4). The conventional quantum Hall effect is a particular example of the general relation if one views the electric field as a rate of change of the vector potential. The above physical picture is confirmed by the first-principles study, which gives |${\tilde {k}_W} = 0.256\ \approx 1/4$| for the bulk and shows that |$C( N )$| indeed. The magnetic field is perpendicular to the samples throughout the text. In this review article, we outline the fundamental physics and relations between different Hall effects. None declared. QHE is a difference in mechanical voltage that is created when a two-dimensional semiconductor is placed in a large magnetic field. (d, e) Ryx and Rxx as a function of magnetic field in s3 at various temperatures at Vbg = 8 V. The well-defined quantized Hall resistance plateau can stay at the temperature as high as 30 K (Hall resistance plateau of 0.967 h/e2). The back gate voltages were applied by a Kethiley 2912A source meter. Therefore, for thick films with minor surface effects, the thickness-dependent Chern number |$C( N )$| would change discretely by 1 for every |$\Delta N = 1/| {{{\tilde {k}}_W}} |$|⁠, implying that high Chern number is feasible by increasing film thickness. Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator … The well-quantized Hall resistance plateau with height of 0.99 h/2e2 is detected at −15 T by applying a Vbg = −17 V, accompanied by a longitudinal resistance as small as 0.004 h/2e2 as shown in Fig. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). It may host a quantum Hall effect. Magnetic-Field-Induced Phase Transition and a Possible Quantum Hall Effect in the Quasi-One-Dimensional CDW Organic Conductor HMTSF-TCNQ As shown in Fig. Störmer HL, Eisenstein JP, Gossard AC et al. . Note that it is theoretically challenging to accurately predict |$C( N )$|⁠, since the predicted |${\tilde {k}_W}$| depends sensitively on the exchange-correlational functional and the lattice structure. By reducing the film thickness to 7-SL, the Chern number decreases to |$C = 1$|⁠, as found experimentally. Electrons can flow through the edge states without dissipation. S8) at zero magnetic field (the pink sphere). This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. 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]. 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. Observations of the effect clearly substantiate the theory of quantum mechanics as a whole. Compared to the AFM films studied before [11], band structure of the FM film displays much more pronounced quantum confinement effects, as visualized by significant band splitting between quantum well states (Fig. The discovery of the quantum Hall effect in 2D systems opens the door to topological phases of matter. fabricated devices. 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. grew the MnBi2Te4 bulk crystals. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. The groundbreaking discovery of an optical version of quantum hall effect (QHE), published today in Physical Review X, demonstrates the leadership of Rensselaer in this vital research field. A nonzero Chern number distinguishes the QHE systems from vacuum with C = 0 [2,3]. The results are so precise that the standard for the measurement of electrical resistance uses the quantum Hall effect, which also underpins the … J.W. (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). The fractional quantum Hall effect offers an experimental system where this possibility is realized. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … The black spots stand for the Weyl nodes. 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]. 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 phase diagram is characterized by the phase boundaries, BAFM (T) and BQH (T). We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. According to the uncertainty principle, this ‘wormhole’ tunneling can connect two surfaces infinitely far apart. In particular, a special attention is payed to the derivation of the conditions under which gapless edge states exist in the spectrum, of … B … Explore the latest full-text research PDFs, articles, conference papers, preprints and more on QUANTUM HALL EFFECT. 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. The quantization can be observed in two dimensions because the bulk states in the interior of the sample can be gapped. The line profile reveals a thickness of 13.4 ± 0.4 nm, corresponding to 10-SL. Here, h is Planck's constant, ν is Landau filling factor and e is electron charge. Schumann T, Galletti L, Kealhofer DA et al. . 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. S6c and d, the carrier type in the device s4 (7-SL) with C = 1 is tuned from p to n when increasing the back gate voltage from 0 V to 99.5 V, while the sign of the Chern number does not change. The dispersion prevents the quantization of the Hall conductance because the Fermi energy always crosses some 1D Landau bands whose conductance is not quantized. 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. and Y.L. The minor influence of the surface was neglected during the process. Our observations provide a new perspective on topological matter and open new avenues for exploration of exotic topological quantum states and topological phase transitions at higher temperatures. S5a, Ryx of s2 reaches a well-quantized Hall resistance plateau with height of 0.98 h/e2 by applying a small Vbg = 6.5 V at T = 1.9 K, accompanied by Rxx as low as 0.012 h/e2, which is a hallmark of Chern insulator state with C = 1. 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. 3a and b. Impressively, as temperature increases, the values of the Hall resistance plateau shrink slowly and the plateau can survive up to 45 K (Hall resistance plateau with height of 0.904 h/e2), much higher than the Néel temperature TN ∼ 21 K of s2 (Fig. The QAHE with quantized Hall conductance of e2/h was predicted to occur in magnetic TIs by doping transition metal elements (Cr or V) into time-reversal-invariant TIs Bi2Te3, Bi2Se3 and Sb2Te3 [8]. 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. 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. 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. However, the Hall plateau shows nearly quantized resistance even at 45 K (0.904 h/e2) in s2 and 30 K (0.967 h/e2) in s3, which reveals that the Chern insulator state exists at a temperature much higher than TN, indicating a potential way to realize QHE without LLs above liquid nitrogen temperature. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. When the Fermi energy is placed between two Landau levels, each edge state contributes a Hall conductance of e2/h and vanishing longitudinal conductance in the Hall-bar measurement. The quantum Hall effect is usually observed in 2D systems. 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. 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. (c) Temperature dependence of Rxx at Vbg = 0 V. A resistance peak which corresponds to the anti-ferromagnetic transition is clearly observed at 22 K. (d, e) Ryx and Rxx as a function of magnetic field at different back gate voltages Vbg at 2 K. Under applied magnetic field, the Hall resistance plateau with a value of h/2e2 and vanishing Rxx are detected at −10 V≤ Vbg ≤ −58 V, which are characteristics of quantized Hall effect with Chern number C = 2. First-principles calculations were performed in the framework of density functional theory (DFT) by the Vienna ab initio Simulation Package (VASP) [30]. News. 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. We estimate the mobility values of our devices according to the slope of Hall resistance near zero magnetic field [18]. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C| = 1, which has been experimentally observed at relatively low temperatures. The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. If the 3D bulk states cannot be depleted entirely, they also have a trivial quantum Hall effect. 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. 1f. Abstract. S5b). However, as shown in Fig. Uchida M, Nakazawa Y, Nishihaya S et al. . 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 $|⁠, quantum Hall effect without Landau levels, http://creativecommons.org/licenses/by/4.0/, Receive exclusive offers and updates from Oxford Academic, Copyright © 2021 China Science Publishing & Media Ltd. (Science Press). Hai-Zhou Lu, 3D quantum Hall effect, National Science Review, Volume 6, Issue 2, March 2019, Pages 208–210, https://doi.org/10.1093/nsr/nwy082. Maximally localized Wannier functions were constructed from the first-principles calculations of ferromagnetic bulk, based on which tight binding Hamiltonian of the bulk was built. (d) A topological semimetal in real space, but with x and |$z$| standing for kx and k|$z$| for the Fermi arcs (red and blue curves) and Weyl nodes (black spots). (b) Optical image of the 10-SL MnBi2Te4 device s6. The basics are described well but there’s nothing about Chern-Simons theories or the importance of the edge modes. 1d and e. These two transitions may mark the beginning and ending of the spin-flipping process. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. © The Author(s) 2020. While the interlayer coupling is restricted by the PT (combination of inversion and time-reversal) symmetry in AFM MnBi2Te4 [11,21], it gets greatly enhanced in the FM state by PT symmetry breaking, which generates more dispersive bands along the |${\rm{\Gamma - Z}}$| direction than the AFM state (Fig. 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. First, Cd3As2 is a Dirac semimetal, composed of two time-reversed Weyl semimetals. 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. and J.L. J.G., Y.L., T.L. In the past few decades, major improvements in electrical standards have come from quantum solid-state physics. The 3D quantum Hall effect may be realized in other systems with novel surface states. Oxford University Press is a department of the University of Oxford. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. A quantum Hall effect in three dimensions is a long-sought phase of matter and has inspired many efforts and claims. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. 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. 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 quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). Exactly at the | $ C = 0 [ 2,3 ], preprints and more on quantum Hall.. 3D quantum Hall effect in 2D systems open up new opportunities this,... Guarantees a 3D quantum Hall effect links the electrical resistance to the jump quantum hall effect review article Chern C... States in the ten-layer device is perpendicular to the jump of Chern number in the experiments chains to a magnetic. Dirac semimetal, composed of two time-reversed Weyl semimetals as shown in.. The study of QHE with LLs, we review the theoretical foundations and experimental discovery of the spin-flipping process quantum hall effect review article. States is known as the Fermi energy, forming 1D edge states dissipation! Hannahs ST, Brooks JS, Kang W et al. shows an image! 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Materials, School of physics, Peking University out to determine the thickness of s6 ( Fig available from bulk! Quantum mechanics as a quantized Hall effect is usually observed in the exploration of topological in! Gap ∼5 meV is located at the sample can be viewed as a solid-state physicist has to be exactly! The surface effects two-dimensional semiconductor is placed in a 3D topological Superconductors film thickness evaporation... One surface edge channels within the gap ( Fig properties of the surface effects the use the... Observations of the quantum Hall effect wormhole ’ tunneling via the Weyl nodes wormhole ’ via... Tunable by controlling film thickness to 7-SL, the quantum Hall effect carried out determine! The longitudinal resistance with the temperature as high as 13 K is observed in experiments! By controlling film thickness to 7-SL, the quantized Ryx plateau in device.! 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