^{2}) and vanishing longitudinal resistance under zero magnetic field (where h is the Planck constant, e is the elementary charge, and the Chern number C is an … DOI:https://doi.org/10.1103/PhysRevLett.71.3697. Download PDF Abstract: Due to the potential applications in the low-power-consumption spintronic devices, the quantum anomalous Hall effect (QAHE) has attracted tremendous attention in past decades. The The quantum spin Hall (QSH) effect is considered to be unstable to perturbations violating the time-reversal (TR) symmetry. IMAGE: ZHAO ET AL., NATURE The quantum anomalous Hall effect is defined as a quantized Hall effect realized in a system without an external magnetic field. PHYSICAL REVIEW LETTERS week ending PRL 97, 036808 (2006) 21 JULY 2006 Quantum Spin-Hall Effect and Topologically Invariant Chern Numbers D. N. Sheng,1 Z. Y. Weng,2 L. Sheng,3 and F. D. M. Haldane4 1 Department of Physics and Astronomy, California State University, Northridge, California 91330, USA 2 Center for Advanced Study, Tsinghua University, Beijing 100084, China 3 Department … The possibility to realize a robust QSH effect by artificial removal of the TR symmetry of the edge states is explored. Quantum Hall effect requires • Two-dimensional electron gas • strong magnetic field • low temperature Note: Room Temp QHE in graphene (Novoselov et al, Science 2007) Plateau and the importance of disorder Broadened LL due to disorder ... carry Hall current (with non-zero Chern number) Quantization of Hall conductance, Laughlin’s gauge argument (1981) 1 2 () 2 ii e i i e e To address this, we have been improving access via several different mechanisms. ... have been well established. Haldane proposed the quantum anomalous Hall effect, which presents a quantized transverse conduc-tivity but no Landau levels [32]. ©2021 American Physical Society. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators). The relation between two different interpretations of the Hall conductance as topological invariants is clarified. Abstract: Due to the potential applications in the low-power-consumption spintronic devices, the quantum anomalous Hall effect (QAHE) has attracted tremendous attention in past decades. Unlike the integer quantum Hall effect, the electronic QAHE requires no external magnetic field and has no Landau levels. The quantum anomalous Hall (QAH) effect is a topological phenomenon characterized by quantized Hall resistance and zero longitudinal resistance (1–4). A striking model of much interest in this context is the Azbel–Harper–Hofstadter model whose quantum phase diagram is the Hofstadter butterfly shown in the figure. In prior studies, the QAH effect had been experimentally realized only in materials where an important quantity called the Chern number had a value of 1, essentially with a single two-lane highway for electrons. Physical Review Letters™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. Quantum Hall effect requires • Two-dimensional electron gas • strong magnetic field • low temperature Note: Room Temp QHE in graphene ... carry Hall current (with non-zero Chern number) Quantization of Hall conductance, Laughlin’s gauge argument (1981) 1 2 () 2 ii e i i e e Information about registration may be found here. The integer here is equal to the Chern number which arises out of topological properties of the material band structure. The relation between two different interpretations of the Hall conductance as topological invariants is clarified. Different from the conventional quantum Hall effect, the QAH effect is induced by the interplay between spin-orbit coupling (SOC) and magnetic exchange coupling and thus can occur in certain ferromagnetic (FM) materials at zero … The (ﬁrst) Chern number associated with the energy band is a topo-logical invariant, which is a quantized Berry ﬂux because Agreement. … In the TKNN form of the Hall conductance, a phase of the Bloch wave function defines U(1) vortices on the magnetic Brillouin zone and the total vorticity gives σxy. Quantum Hall Effect on the Web. The integers that appear in the Hall effect are examples of topological quantum numbers. Analyzing phase … In this chapter we will provide introductory accounts of the physics of the fractional quantum Hall effect, the mathematical origin of the Chern-Simons forms (which arise from the Chern classes … The amazingly precise quantization of Hall conductance in a two-dimensional electron gas can be understood in terms of a topological invariant known as the Chern number. the user has read and agrees to our Terms and The integer here is equal to the Chern number which arises out of topological properties of the material band structure. ... By analyzing spin Chern number and calculating the energy spectra, it is presented that when RSOC, spin-independent and spin-dependent staggered potentials are introduced into the Lieb lattice, a topological nontrivial gap between the flat bands will be opened and the QAH effect may occur. The first Topological Insulator is shown in Integer quantum Hall effect. Joseph Avronis a professor of physics at the Technion—Israel Institute of Technology, in Haifa. Quantum anomalous Hall effect is the "quantum" version of the anomalous Hall effect. The Chern-Simons form can be used as the Lagrangian in an effective field theory to describe the physics of fractional quantum Hall systems. We present a topological description of the quantum spin-Hall effect (QSHE) in a two-dimensional electron system on a honeycomb lattice with both intrinsic and Rashba spin-orbit couplings. The quantum Hall effect without an external magnetic field is also referred to as the quantum anomalous Hall effect. We review some recent developments in the search of the QSH effect in the absence of the TR symmetry. It provides an efficient method of computing (spin) Hall conductances without specifying gauge-fixing conditions. Over a long period of exploration, the successful observation of quantized version of anomalous Hall effect (AHE) in thin film of magnetically doped topological insulator (TI) completed a quantum Hall trio—quantum Hall effect (QHE), quantum spin Hall effect (QSHE), and quantum anomalous Hall effect (QAHE). A Chern insulator is 2-dimensional insulator with broken time-reversal symmetry. These effects are observed in systems called quantum anomalous Hall insulators (also called Chern insulators). Such a nonvanishing Chern number char-acterizes a quantized Hall conductivity and conﬁrms the QAHE in the TMn lattice. In the case of integer quantum Hall states, Chern number is simply the Hall conductance up to a constant. 2 The nonzero Chern number can also be manifested by the presence of chiral edge states within the … A prototypical Chern insulator is the Qi-Wu-Zhang (QWZ) model [49]. One is the Thouless--Kohmoto--Nightingale--den Nijs (TKNN) integer in the infinite system and the other is a winding number of the edge state. Chern number, and the transverse conductivity is equal to the sum of the Chern numbers of the occupied Landau levels. "This unique property makes QAH insulators a good candidate for use in quantum computers and other small, fast electronic devices." / Afterwards, Haldane proposed the QHE without Landau levels, showing nonzero Chern number |C|=1, which has been experimentally observed at relatively low The Quantum Hall Effect by Steven Girvin Quantum Hall Effects by Mark Goerbig Topological Quantum Numbers in Condensed Matter Systems by Sebastian Huber Three Lectures on Topological Phases of Matter by Edward Witten Aspects of Chern … Subscription The nontrivial QSHE phase is identified by the nonzero diagonal matrix elements of the Chern number matrix (CNM). Conditions and any applicable Use of the American Physical Society websites and journals implies that For the proof of this equality, we consider an exact sequence of C * -algebras (the Toeplitz extension) linking the half-plane and the planar problem, and use a duality theorem for the pairings of K-groups with cyclic cohomology. 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 valley Chern numbers of the low-energy bands are associated with large, valley-contrasting orbital magnetizations, suggesting the possible existence of orbital ferromagnetism and anomalous Hall effect once the valley degeneracy is … Under a gap condition on the corresponding planar model, this quantum number is shown to be equal to the quantized Hall conductivity as given by the Kubo–Chern formula. The Quantum Hall … We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. A team of researchers from Penn State has experimentally demonstrated a quantum phenomenon called the high Chern number quantum anomalous Hall (QAH) effect. https://doi.org/10.1103/PhysRevLett.71.3697, Physical Review Physics Education Research, Log in with individual APS Journal Account », Log in with a username/password provided by your institution », Get access through a U.S. public or high school library ». We consider the integer quantum Hall effect on a square lattice in a uniform rational magnetic field. The nontrivial QSHE phase is … [2], Effect in quantum mechanics where conductivity acquires quantized values, https://en.wikipedia.org/w/index.php?title=Quantum_anomalous_Hall_effect&oldid=929360860, All Wikipedia articles written in American English, Creative Commons Attribution-ShareAlike License, This page was last edited on 5 December 2019, at 09:14. The quantum Hall effect refers to the quantized Hall conductivity due to Landau quantization, as observed in a 2D electron system [1]. The (ﬁrst) Chern number associated with the energy band is a topo-logical invariant, which is a quantized Berry ﬂux because The vertical axis is the strength of the magnetic field and the horizontal axis is the chemical potential, which fixes the electron density. 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. 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