Electrons can flow through the edge states without dissipation. The Fermi-arc surface states form a unique 2D electron gas, half from the top surface and half from the bottom surface (Fig.Â 1c and d). 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. Rev. 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. 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. In this work, the MnBi2Te4 flakes were mechanically exfoliated from high-quality MnBi2Te4 single crystals. 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). The quantum Hall effect links the electrical resistance to the elementary charge and the Planck constant. The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without external magnetic field. Different schemes have been proposed to gap the 3D bulk states for the quantization of the Hall conductivity in three dimensions [2,3]. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. B … The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. A prefactor of the activated dissipative conductivity in the quantum Hall regime is studied in the case of a short-range random potential. 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. MnBi2Te4 is a layered material which can be viewed as a layer of Bi2Te3 TI intercalated with an additional Mn-Te layer [11–20]. 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. This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. 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 Planckâs constant, and n is an integer known as the âChern numberâ (named after the mathematician Shiing-Shen Chern). 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. 3 and Fig. 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. Explore the latest full-text research PDFs, articles, conference papers, preprints and more on QUANTUM HALL EFFECT. Second, the 3D bulk states quantize 2D subbands for those thicknesses. The black and red traces represent magnetic field sweeping to the positive and negative directions, respectively. These two issues may explain the 2-fold and 4-fold degenerate Hall resistance plateaus observed in the experiments. The conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … Oxford University Press is a department of the University of Oxford. By reducing the film thickness to 7-SL, the Chern number decreases to |$C = 1$|⁠, as found experimentally. As a result, there are no Landau levels, edge states, or quantum Hall effect on one surface. 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. Standard electron beam lithography in a FEI Helios NanoLab 600i Dual Beam System was used to define electrodes after spin-coating PMMA resist. 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. We estimate the mobility values of our devices according to the slope of Hall resistance near zero magnetic field [18]. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. In a strong magnetic field, the energy spectrum of a 2D electron gas is quantized into Landau levels. 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 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. (b) Optical image of the 10-SL MnBi2Te4 device s6. 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. The high-temperature QHE without LLs is also observed in the 8-SL device s3. 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. 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. Nevertheless, several questions still hold. 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. 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. 4b). 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. These observations unambiguously demonstrate that the observed quantized Hall resistance plateau has nothing to do with LLs and the quantized Ryx originates from Chern insulator state. An alternative mechanism of realizing QAHE through localization of band electrons was later proposed in 2003 [7]. Zhang H, Freimuth F, Bihlmayer G et al. 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 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 … grew the MnBi2Te4 bulk crystals. Atomic force microscope measurements were carried out to determine the thickness of s6 (Fig. According to the uncertainty principle, this âwormholeâ tunneling can connect two surfaces infinitely far apart. 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. 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. Possible signatures of the 3D quantum Hall effect have been observed … 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]. Based on the mBJ functional [29], we systematically tested the influence of lattice parameter |${c_0}$| on band structure and |$C( N )$| (Fig. The 1D edge states in this 3D quantum Hall effect show an example of (d â 2)-dimensional boundary states. A review article about my career as a solid-state physicist has to focus on the quantum Hall effect (QHE). The green and orange arrowed lines depict the edge states of the 3D quantum Hall effect. 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. and Y.W. and J.L. News. 1d) and s7 with p-type carriers (Fig. The edge-state calculation reveals that there exist two chiral gapless edge channels within the gap (Fig. In the past few decades, major improvements in electrical standards have come from quantum solid-state physics. performed transport measurements. Contrariwise, the increase of film thickness could lead to higher Chern numbers (⁠|$C > 2$|⁠), which is awaiting experimental confirmation. Otrokov MM, Rusinov IP, Blanco RM et al. 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. We review recent results concerning the spectrum of edge states in the quantum Hall effect in graphene. 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. Weyl points (WPs) with topological charge of +1 and −1 are denoted by blue and red circles in the top panel, respectively. 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. High-Chern-number QHE without LLs has never been observed experimentally. J.G., Y.L., J.L., Y.X. It is obvious that the AFM state disappears at TN. The temperature dependence of longitudinal resistance Rxx is shown in Fig. Theoretical proposals based on the intrinsic band structure of 2D systems open up new opportunities. The 8-SL is the marginal case, which has |$C = 1$| in experiment and |$C = 2$| in theory. 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. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. 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. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. 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. Hall effect in graphene. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number | C | = 1, which has been experimentally observed at relatively low temperatures. Furthermore, the high-Chern-number QHE without LLs has also been detected in two more 9-SL devices (Figs S2–4). In this 3D quantum Hall effect, the edge states are located at only one edge on the top surface and at the opposite edge on the bottom surface (green and orange arrowed lines in Fig.Â 1d and e), which can be probed by scanning tunneling microscopy. (a) Crystal structure of MnBi2Te4. Find methods information, sources, references or conduct a literature review … increases by 1 for every |$\Delta N = 4$| (Fig. 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]. The discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. There may also be a trivial quantum Hall effect on a single surface. 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 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. Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. 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. Our discoveries break new ground in the exploration of topological quantum states and provide a platform for potential applications in related low-consumption electronics. (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). Besides, the requirement of ultralow temperatures limits the study of QHE without LLs. (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. 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]. 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. This indicates that QHE can be realized without the formation of LLs. 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