(c, d) Band structure and edge states along the (100) direction in the 9-SL film. Hai-Zhou Lu, 3D quantum Hall effect, National Science Review, Volume 6, Issue 2, March 2019, Pages 208â210, https://doi.org/10.1093/nsr/nwy082. 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). A prefactor of the activated dissipative conductivity in the quantum Hall regime is studied in the case of a short-range random potential. It furthers the University's objective of excellence in research, scholarship, and education by publishing worldwide, This PDF is available to Subscribers Only. None declared. 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. The quantum Hall effect has led to three Nobel Prizes in Physics (1985 von Klitzing; 1998 Tsui, Stormer, Laughlin; 2016 Thouless, Haldane, Kosterlitz). where |${c_0}\ $|is the out-of-plane thickness of each SL, and |${\tilde {k}_W} = | {{k_W}} |\ {c_0}/\pi $|. (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 quantum Hall effect in three dimensions is a long-sought phase of matter and has inspired many efforts and claims. 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 quantized plateaus from 1.9 K to 30 K are very clear and overlapped. 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 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]. (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 discovery of the quantum Hall effect (QHE) marked a turning point in condensed-matter physics. The quantum anomalous Hall effect is a novel manifestation of topological structure in many-electron systems and may have potential applications in … Then, tight binding Hamiltonians of thin films were obtained by means of cutting slabs from the bulk. Scale bar represents 10 μm. (c) B-T phase diagram of s2. The discovery of QHE introduces the concept of topology into condensed matter physics and is extremely important to physical sciences and technologies. The measurement of the Hall resistance showed that electronic resistance could be defined precisely in terms of fundamental constants, even in a disordered and irregular sample. (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). Obviously, one would never obtain high Chern number C > 1 in AFM MnBi2Te4. S9), and finally decided to use the experimental value |${c_0} = 13.6$| Å. QHE is a difference in mechanical voltage that is created when a two-dimensional semiconductor is placed in a large magnetic field. 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 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. The edge-state calculation reveals that there exist two chiral gapless edge channels within the gap (Fig. J.G., Y.L., T.L. 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]. All data analyzed to evaluate the conclusions are available from the authors upon reasonable request. For full access to this pdf, sign in to an existing account, or purchase an annual subscription. J.W. S9). 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 high-temperature QHE without LLs is also observed in the 8-SL device s3. The conditions that affect the accuracy attained in reproducing the quantum values of the resistance and characteristics of semiconductor structures (silicon MOS structures and … (b) Optical image of the 10-SL MnBi2Te4 device s6. However, the rigorous conditions of ultrahigh mobility, ultralow temperature and strong external magnetic field limit the deep exploration and wide applications of QHE. As shown in Fig. The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. In this perspective, we review our proposal that guarantees a 3D quantum Hall effect. J.G. 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. Schumann T, Galletti L, Kealhofer DA et al.Â . 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 basics are described well but there’s nothing about Chern-Simons theories or the importance of the edge modes. 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. 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. The QHE in 2D electron systems with high mobility is originated from the formation of Landau levels (LLs) under strong external magnetic field. Theoretical proposals based on the intrinsic band structure of 2D systems open up new opportunities. StÃ¶rmer HL, Eisenstein JP, Gossard AC et al.Â . The quantum anomalous Hall (QAH) effect, considered as a quantized version of anomalous Hall effect discovered in 1881 [ 7 ], has been theoretically proposed for magnetic topological insulators (TIs) [ 8 – 13 ], where the ferromagnetic ordering and spin–orbit coupling (SOC) are sufficiently strong that they can give rise to a topologically non-trivial phase with a finite Chern number. The theory suggests that the topological Chern number is tunable by controlling film thickness of FM MnBi2Te4. 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. As shown in Fig. Here, to improve the description of electronic band structure, the mBJ functional [29] was employed to study ferromagnetic bulk MnBi2Te4. 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. 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. In this way, the top and bottom Fermi arcs together support a complete cyclotron motion and the quantum Hall effect. 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. Temperature dependence of the high-Chern-number QHE without LLs in s6. 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. 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. In figure 12(a) the peak mobility as a function of temperature is shown for these generations of growth. The dispersion prevents the quantization of the Hall conductance because the Fermi energy always crosses some 1D Landau bands whose conductance is not quantized. 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}} |$|, implying that high Chern number is feasible by increasing film thickness. and Y.W. However, when MnBi2Te4 is driven from AFM to FM states by external magnetic field, physical properties of the material change dramatically. Since then, Haldane proposed the QHE without Landau levels, showing nonzero Chern number | C | = 1, which has been experimentally observed at relatively low temperatures. Weyl points (WPs) with topological charge of +1 and −1 are denoted by blue and red circles in the top panel, respectively. Nevertheless, several questions still hold. This is like the wormhole effect, which connects 3D spaces via higher-dimensional singularities. Subsequently, the exact quantization was explained by Laughlin based on gauge invariance and was later related to a topological invariance of the energy bands, which is characterized by Chern number C [2–5]. More research will be necessary to verify the mechanism and realize the 3D quantum Hall effect in the future. A review article about my career as a solid-state physicist has to focus on the quantum Hall effect (QHE). A quantum confinement induced gap ∼5 meV is located at the |${\rm{\Gamma }}$| point. Wan X, Turner AM, Vishwanath A et al.Â . Hall effect in graphene. We illustrate our findings by analyzing the response of interacting spin chains to a rotating magnetic field. 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. 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. 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. Which has the special property that it lives in fractal dimensions as a layer of TI... Resistance to the jump of Chern number C > 1 in AFM.. Single crystals using scotch tape quantum hall effect review article quality of mm-sized MnBi2Te4 crystals was examined on a single surface, a... 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