S9), and finally decided to use the experimental value |${c_0} = 13.6$| Å. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number | C | = 1, which has been experimentally observed at relatively low temperatures. increases by 1 for every |$\Delta N = 4$| (Fig. Atomic force microscope measurements were carried out to determine the thickness of s6 (Fig. According to the uncertainty principle, this ‘wormhole’ tunneling can connect two surfaces infinitely far apart. These two issues may explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the experiments. 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]. We show that the Fermi arcs can give rise to a distinctive 3D quantum Hall effect in topological semimetals. (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. 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. 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. 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. The discrete increase of Chern number with increasing film thickness is a generic feature of ferromagnetic Weyl semimetals, which can also be understood by the topological band inversion picture as discussed in Methods. (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. 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). Find methods information, sources, references or conduct a literature review … 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. 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. Störmer HL, Eisenstein JP, Gossard AC et al. . 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 proposal employs topologically protected Fermi arcs and ‘wormhole’ tunneling via the Weyl nodes in a 3D topological semimetal. 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). 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. 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]. Magnetic-Field-Induced Phase Transition and a Possible Quantum Hall Effect in the Quasi-One-Dimensional CDW Organic Conductor HMTSF-TCNQ 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). 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. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. 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. (c, d) Band structure and edge states along the (100) direction in the 9-SL film. 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 discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. This quantization temperature is the highest record in systems showing QHE without LLs. 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 … MnBi2Te4 is a layered material which can be viewed as a layer of Bi2Te3 TI intercalated with an additional Mn-Te layer [11–20]. and J.L. When further increasing Vbg to 10 V, the quantized Hall resistance plateaus remain robust as shown in Fig. 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. The quantized plateaus from 1.9 K to 30 K are very clear and overlapped. In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. 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. 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). A prefactor of the activated dissipative conductivity in the quantum Hall regime is studied in the case of a short-range random potential. The 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. The fractional quantum Hall effect offers an experimental system where this possibility is realized. 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]. 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. In general, the Chern number in ordinary QHE corresponds to the occupancy of LLs and the sign of the Chern number will change once the carrier type is switching. wrote the manuscript with input from all authors. 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. More research will be necessary to verify the mechanism and realize the 3D quantum Hall effect in the future. 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. 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. Y.X. (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). A review article about my career as a solid-state physicist has to focus on the quantum Hall effect (QHE). Otrokov MM, Klimovskikh II, Bentmann H et al. 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. 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. High-temperature QHE without LLs in MnBi2Te4 devices s2 (7-SL) and s3 (8-SL). With further application of a perpendicular magnetic field, the sample is supposed to enter the perfectly aligned FM state [19]. 1d and e. These two transitions may mark the beginning and ending of the spin-flipping process. S9). 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. 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. In this article, we review the theoretical foundations and experimental discovery of the quantum spin Hall effect. Nevertheless, several questions still hold. 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. Schumann T, Galletti L, Kealhofer DA et al. . where |${c_0}\ $|is the out-of-plane thickness of each SL, and |${\tilde {k}_W} = | {{k_W}} |\ {c_0}/\pi $|⁠. In this review article, we outline the fundamental physics and relations between different Hall effects. Furthermore, for the C = 2 devices, the quantized Ryx plateau in device s6 with n-type carriers (Fig. News. J.G. Figure 1b shows an optical image of the MnBi2Te4 device (s6) with Hall bar geometry. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. 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. 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. J.G., Y.L., T.L. 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