Because of the existence of these edge states, upon sending a flux quanta h/e, by gauge invariance and explicit calculating of the Landau level wave functions, in each Landau level one state is "pushed from the bulk to the edge" and increases energy. Heuristically this is sort of like a hybrid between spin and charge Hall effects. 2011. Jan 07, 2008 · The Quantum Spin Hall Effect: Theory and Experiment. The QSH phase consists of a 2D bulk with an inverted (topological) gap, which gives rise to topologically protected counterpropagating helical edge states related by TRS. Jun 26, 2015 · The spin—a measure of the intrinsic angular momentum—can be thought of as an equivalent of the spin of a top. Hall effect. The purpose of this quiz is to give you room to test yourself regarding your knowledge in quantum spin Hall effect. Condens. The flow of information is loss-free, even for slight irregularities. Graphene, the Quantum Spin Hall Effect and topological insulators. • Natural generalization of the quantum Hall effect. We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride cadmium telluride semiconductor quantum wells. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. • A special class of Topological Insulators that contain edge states that are spin filtered. Quantum spin Hall effect. Topology in Condensed Matter. In the integer and fractional quantum Hall effects, the electric current flows through a thin layer under the strong magnetic field. The quantum-mechanical wave nature of the travelling electrons organises them into neat channels along the edges of the sample. The materials which exhibit quantum Hall effect such as graphene, are like atoms, May 04, 2015 · Figure 1: (Left) The quantum Hall effect (QHE) occurs in a two-dimensional electron system under a large applied magnetic field. It exhibits the quantum spin Hall effect, in which an electric current can induce a transverse spin current or spin accumulation near the system boundary. The quantum spin Hall effect was first proposed by Kane and Mele in 2005. The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. The electron transport in Quantum Hall effect can be seen in analogy to atomic physics. We note that this is the highest temperature at which the main hallmark of the QSHI state has ever been observed. 2t M=1, N=100 Ballistic The spin Hall effect is seen in electrons and other quantum particles when their motion depends on their magnetic orientation, or "spin. • That is one edge state made up of spin up carriers and another edge state made up of spin down carriers. Andrei Bernevig and Shou-Cheng Zhang Department of Physics, Stanford University, Stanford, California 94305, USA (Received 18 April 2005; published 14 March 2006) The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. 55 meV, much higher than that of graphene. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. 00 / 3 votes) Translation Find a translation for Quantum Spin Hall Stanford physics Professor Shoucheng Zhang says a new generation of semiconductors, designed around the phenomenon known as the Quantum Spin Hall Effect, could keep Moore’s law in force for decades to come. Here we review a recent theory which predicts that the QSH state can be realized in HgTe/CdTe semiconductor quantum wells (QWs). These edge channels are protected by time reversal symmetry and spin currents propagate without dissipation. Kane and Mele: Quantum Spin Hall effect. Inversion symmetry breaking (not really needed. Quantum spin Hall effect. To study this phenomenon, scientists apply a large magnetic field to a 2D (sheet) semiconductor. Jan 9, 2018 Quantum anomalous Hall-quantum spin Hall effect in optical superlattices. Jul 11, 2018 · The quantum Hall effect in two-dimensional electron gases involves the flow of topologically protected dissipationless charge currents along the edges of a sample. (2DTI) exhibit quantum spin Hall (QSH) eﬀect with spin-ﬁltered edge states in the bulk gap. Quantum spin Hall (QSH) effect materials feature edge states that are topologically protected from backscattering. A quantum circuit might use spins, described as The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. The transverse resistance (ρ x y) takes on quantized values while the longitudinal resistance (ρ x x) vanishes. The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. Science, 314,1757 (2006). Shou-Cheng Zhang. However, the quantized spin Hall current is not Sep 30, 2011 Figure 1: Electrons at the edge of the material mercury-telluride exhibit the quantum spin Hall effect, in which two oppositely spin-polarized The Effect of Interactions on a Topological Insulator. In the quantum Hall effect, the states with zero and one flux Spin Hall Effect Graphene can filter electrons according to the direction of their spin Researchers from MIT discovered that under a powerful magnetic field and at very low temperatures, graphene can filter electrons according to the direction of their spin. Quantum Hall effects, Electrical injection of spin polarized carriers, Fullerenes and related materials, Magnetoelectronics, spintronics: devices exploiting spin polarized transport or integrated magnetic fields Keywords: quantum spin Hall, topological insulators, quantum state, nonmagnetic insulators, pure spin current, nonmagnetic disorder Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. The team was intrigued to learn that an analogy for these can be found for photons. InSb and InSb quantum wells QWs have drawn attention in several developments, ranging from the quest for new electronic devices,1,2 to mag-netoresistive devices3,4 and spin-based electronics. Stanford University with Andrei Bernevig, Taylor Hughes. quantum spin Hall (QSH) effect has been theoretically predicted and experimentally observed in HgTe quantum wells (QW) [8,9]. The Quantum Spin Hall Effect. r + ½(Hr + rH). West Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544, USA (Received 18 January 2017; published 4 May 2017) the quantum spin Hall effect of light . the quantum spin Hall effect (QSHE) by exploiting adiabatic continuity and the direct calculation of the Z2 topological invariant. I really don't understand how does the current couple through the interaction. With the hydrogen (H) 30,31 , halogens (F, Cl, Br, I) 31 or methyl (CH The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall effect. Rev. The quantum phase transition at the critical thickness, nm, is also independently determined from the occurrence of a magnetic field induced insulator to metal transition. Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator Son-Hsien Chen,1,2,* Branislav K. Based on the orientation of their spin, the electrons existing in a spin current are deflected sideways. 5 Here we present low-temperature measurements of the spin-dependent quantum-interference effect of antilocalization AL in InSb quantum wells. conventional quantum Hall effect, this quantum anomalous Hall effect (QAHE) can occur only in two-dimensional systems that are not time-reversal invariant. The diagonal resistance becomes very small at integer and specific fractional filling factors where the electron scatterings are very few. A “quantum spin hall effect” is seen in graphene with the spin-orbit term included. e. Spin hall effect is the accumulation of spin on the boundaries. Researchers have reported the first observation of the "spin Hall effect" in a Bose-Einstein condensate, a cloud of ultracold atoms acting as a single quantum object. x x • Insulating gap in the bulk. QUANTUM PHYSICS New spin on the Hall effect Andrew D. Quantum Hall Spin Diode J. The potential arises because a transverse electric field must accelerate the current radially to follow the curve. I. Quantum spin Hall effect in two-dimensional hydrogenated SnPb alloy films Miaojuan Ren ,* a Min Yuan , a Xinlian Chen , a Weixiao Ji ,* a Ping Li a and Feng Li a In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. The importance of the negative spin has been discussed. The spin Hall effect in a quantum gas M. 5−7 More importantly, this topological phase requires neither strong electron−electron interaction nor strong magnetic ﬁeld to manipulate spin transport, demonstrating a potential paradigm shift in the spintronic devices. We predict that the QSHE can be observed in an experimentally accessible low temperature regime in silicene with the spin-orbit band gap of 1. The quantum version of the Spin Hall effect is the quantum spin Hall effect . This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed matter science. It is shown that the ac QSH effect can be interpreted as a bulk quantum pumping effect. It is the "coupling constant" or measure of the strength of the electromagnetic force that governs how electrically charged elementary particles (e. The essential ingredient for pro-ducing the quantum Hall effect is the breaking of the time-reversal symmetry, usually by applying an external magnetic ﬁeld. Spin-Orbit Coupling and Quantum Spin Hall Effect for Neutral Atoms without Spin Flips Colin J. Abstract: This talk provides a brief and pedagogical overview to some aspects of -time- parity symmetric optics, extraordinary momentum and spin in evanescent waves, optical analog of Quantum hall effect y z xy x E B j ne Each Landau level can hold the same number of electrons. We show that electric current flowing through a curved wire produces a transverse electric potential across the wire. Astonishingly, the spin currents flow without any external stimulus as a result of the internal structure of the material. Liu 1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China • Quantum Hall effect exists in D=2, due to Lorentz force. III. The 1 2 4e2 h offset, The quantum anomalous Hall effect or mag-netic topological insulator corresponds to the quantum Hall effect without applying external magnetic ﬁeld [1–3], and ex-hibits immense application potential in dissipationless quan-tum electronics [4–8]. B. Graphene with structure-induced spin-orbit coupling: Spin-polarized states, spin zero modes, and quantum Hall effect Emmanuel I. Quantum spin Hall effect From Wikipedia, the free encyclopedia The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors that have a quantized spin-Hall conductance and a vanishing charge-Hall conductance. There is also the quantum spin Hall effect Jan 5, 2018 A variety of monolayer crystals have been proposed to be two-dimensional topological insulators exhibiting the quantum spin Hall effect Dec 5, 2018 A lot--if not most--of quantum states of condensed matter are classified by the symmetries they break. E. In particular, the intrinsic spin Hall effect promises the possibility of designing the intrinsic electronic properties of materials so that the effect can be maximized. quantum spin Hall effect (QSHE), a new quantum state of matter with a nontrivial topological property, due to its scientiﬁc importance as a novel quantum state and the technological applications in spintronics. It benefits from insulators feature edge states, topologically protected from backscattering by time-reversal symmetry. The researchers aim to use the homogeneous heterostructures with atomically sharp interfaces and intrinsic magnetic properties to study exotic phenomena such as the quantum anomalous Hall effect Quantum Spin Hall (QSH) has potential applications in low energy consuming spintronic devices and has become a researching hotspot recently. We find that in an We demonstrate that these compounds are characterized by a negative band- bending effect and by the two-dimensional quantum Hall state penetrating deeply The system has a quantized spin current between terminals 3 and 4, hence the name "quantum spin Hall effect". The previous QSHE is protected by the time-reversal (T) invariance. Nikolić,1 and Ching-Ray Chang2,† 1Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA • A new type of dissipationless quantum spin transport. , in non‐magnetic materials and without the application of external magnetic field). Miscellaneous » Unclassified. charlex. That's it. 2. This is a geometric effect in which no magnetic field is present However, so-called nonlinear effects in the oscillations lead to the spin Hall effect not working properly in practical applications -- one reason why scientists have not yet been able to realize Hence, by utilizing gauge fields, this theory provides a unifying physical picture of ``intrinsic'' and ``topological'' anomalous Hall effects, spin-Hall effects, and the general interplay between topological behaviors of electronic and magnetic degrees of freedom. R. The intrinsic spin Hall effect. Jun 26, 2015 · The quantum spin Hall effect is a fundamental property of light In a paper that crystalizes knowledge from a variety of experiments and theoretical developments, scientists from the RIKEN Center for Emergent Matter Science (CEMS) in Japan have demonstrated that the quantum spin Hall effect—an effect known to take place in solid state physics—is also an intrinsic property of light. Spin orbit term connecting Unconventional Quantum Hall Effect in Graphene Zuanyi Li Department of Physics, University of Illinois at Urbana-Champaign, Urbana 61801 Abstract Graphene is a new two-dimensional material prepared successfully in experiments several years ago. Lee, Leonid S. Although its appearance is dependent on electronic structure details, the QAHE is a possibility in any strongly spin-orbit coupled magnetic two-dimensional electron system. CE SHANG,1,2,4 XIANFENG CHEN,1,2 WEIDONG LUO,3 AND FANGWEI YE1,2,*. By contrast, topological states of matter evade traditional symmetry-breaking classification schemes, and they signal the existence of a fundamentally different organizational principle of quantum matter. A quantum spin Hall system possesses a pair of helical edge states. Potential ψ (r) to H in Kubo approach. 2011-09-08 00:00:00 The original motivation of great interest to topological insulators was the hope to observe the quantum spin Hall effect. • U(1) to SU(2), 2D to 3D. Guterding Phenomenology of the QSHE Materials showing QSHE Properties of CdTe and HgTe Quantum Well Structures Experiments Conclusion Literature The Quantum Spin Hall E ect in HgTe/CdTe Quantum Wells German National Academic Foundation, Summer Academy Salem 2012 Daniel Guterding August The researchers succeeded for the first time in directly measuring the spin of electrons in a material that exhibits the quantum spin Hall effect, which was theoretically predicted in 2004 and first observed in 2007. Independently, a quantum spin Hall model was proposed by Bernevig and Zhang in an intricate strain architecture which engineers, due to spin-orbit coupling, a magnetic field pointing upwards for spin-up electrons and a magnetic field pointing downwards for spin-down electrons. The kagome lattice: (a) homogeneous conﬁguration, (b) its dispersion diagram featuring two Dirac cones between the ﬁfth and sixth bands at K and K, (c) folded dispersion diagram featuring a double Dirac cone at the point, (d) the corresponding perturbed Quantum Spin Hall Effect and Topological Phase Transition in HgTeQuantum Wells Taylor L. This chapter begins with a description of quantum spin Hall systems, or topological insulators, which embody a new quantum state of matter theoretically proposed in 2005 and experimentally observed later on using various methods. M. Chern number Gap: Shoucheng Zhang Bernevig, Hughes, Zhang, Science 314, 1757 (2006) Spin-polarized Edge states Andrei Bernevig Quantum Spin Hall Effect It is unusual for a pure-theory physics paper to make it into the journal Science. The phenomenon is crucial to spin-based electronics, and its electrical signal has just been spotted. The quantum spin Hall effect (QSHE) has formed the seed for contemporary research on topological quantum states of matter. Sep 26, 2007 · The quantum spin Hall effect (QSHE) is a related phenomenon that has been predicted to occur not in conductors, but in certain very thin insulators. This type of electronic transport is called the quantum spin hall effect [1]. So when one does, it’s worth a closer look. gap Quantum Spin Hall Insulator and Rashba-Dresselhaus Effect. RIKEN, Saitama, Japan, and The University of Michigan, Ann Arbor, USA . Padilha,1, † and A. The quantum Hall effect is an example of a phenomenon having topological features that can be observed in certain materials under harsh and stringent laboratory conditions (large magnetic field, near absolute zero temperature). The quantum spin Hall state is a state of As you can observe from the figure only Ti,i+1 and Ti+1,i will be nonzero. The researchers succeeded for the first time in directly measuring the spin of electrons in a material that exhibits the quantum spin Hall effect, which was theoretically predicted in 2004 and first observed in 2007. The quantum spin Hall state is a state of the matter proposed to exist in special, and two-dimensional semiconductors. Nikolić,1 and Ching-Ray Chang2,† 1Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716-2570, USA Spin Hall Effects Observation “The orientation of the electrons in the spin layer can be detected by paramagnetic resonance, by the nuclear magnetization resulting from the Overhauser effect, and by the change produced in the surface impedance by the gyrotropyof the spin layer. Molenkamp, Taylor L Hughes , Chao Xing Liu, Xiao Liang Qi, Shou Cheng Zhang Physics Quantum anomalous Hall-quantum spin Hall effect in optical superlattices CE SHANG,1,2,4 XIANFENG CHEN,1,2 WEIDONG LUO,3 AND FANGWEI YE1,2,* 1The State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Quantum Spin Hall Effect. g. Kent The spin Hall effect occurs when electrons with opposite spins go their separate ways in an electric field. 71 Quantum Spin Hall Effect. In the Laughlin argument, which essentially applies only to non-interacting disordered electrons (i. Quantum Spin Hall Effect - Spin orbit induced energy gap in graphene ⇒A new 2D electronic phase - Gapless Edge states and transport - Time Reversal symmetry and Z 2 topological stability. Kennedy, Georgios A. A. Quantum Spin Hall effect in HgTe QWs. 2. But note that time reversal symmetry is broken in such a system. Generalization of the quantum Hall effect. The quantum Hall effect refers to the quantized Hall conductivity due to Landau quantization, as observed in a 2D electron system [1]. The quantum spin Hall effect and topological insulators In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. 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 Why R H has to be exactly (h/e2)/n ? • see Laughlin’s argument below ()kT Bc<=ω Filling factor Aoki, CMST 2011 The The completion of quantum Hall trio, namely the quantum Hall effect (QHE), the quantum spin Hall effect (QSHE), and the quantum anomalous Hall effect (QAHE), has greatly broadened our understandings about the electron movement in solids. Jul 5, 2016 We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. The Spin Hall Effect is the Accumulation of Spin on Boundaries The Hall effect has electrons accumulated on the boundaries. Molecule dynamics results unravel that g-TlA monolayers remain stable even at room temperature. This makes it viable to efficiently produce and regulate the spin waves present in magnetic nano-devices. As the theory for the quantum spin Hall effect predicts that the edge states are robust to The quantum Hall effect is an example of a phenomenon having topological In the case of topological insulators, this is called the spin quantum Hall effect. The team used several sets of lasers to trap rubidium atoms in a tiny cloud, about 10 micrometers on a side, inside a vacuum chamber and then cool the atoms to a few billionths of a degree above absolute zero. These results prove that the quantum spin Hall effect can be induced by an external electric field in silicene, which may have certain practical significance in applications for future spintronics device. The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values Dec 12, 2014 · Quantum spin Hall (QSH) effect materials feature edge states that are topologically protected from backscattering. Such topological states with spin-momentum locking gave rise to a new class of materials: topological insulators (7, 8). II. Therefore if a material is in the topological insulator state they frequently call it the quantum spin Hall state. g-TlA (A = As, Sb) monolayers are found TIs under the influence of strong spin orbit couplings with large bulk band gaps of 131 and 268 meV, respectively. The quantum Hall effect (or integer quantum Hall effect) is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance G undergoes certain quantum Hall transitions to take on the quantized values Jun 05, 2013 · First observation of spin Hall effect in a quantum gas is step toward 'atomtronics'. AKLT state (or Haldane phase) in a spin-1 chain represents a large class of gapped topological paramagnets, which hosts symmetry-protected gapless excitations on the bou port measurement reveals quantum-Hall conductance plateaus (the integer quantum Hall effect) at values G xy~ne 2 h for filling factors n~n s B h e ~4(nz1=2) where all available states up to the nth Landau level are occupied. P. alternate case: quantum spin Hall effect. The simplest explanation of this phenomenon was based on an independent electron picture. 2:31-53. iλλλSO +M-M Spinful fermions in a Graphene-like lattice model: 4-band model. N. The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see Landau quantization). • Standard semiconductors with a strain gradient, narrow gap Jun 13, 2013 · Such spin-Hall effects have been observed for electrons ﬂowing in materials such as GaAs or InGaAs [5, 6]; for laser light traversing dielectric junctions [7]; and now for the ﬁrst time in quantum gases moving through an optical ﬁeld. The striking feature of the integer quantum Hall effect is the persistence of the quantization (i. The source code for the WIKI 2 extension is being checked by The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. The quantum spin Hall effect and topological insulators Xiao-Liang Qi and Shou-Cheng Zhang In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Matter Phys. The quantum spin Hall (QSH) effect describes the state of matter in certain 2D electron systems, in which an insulating bulk state arises together with helical states at the edge of the sample. Sep 26, 2007 Physicists in Germany and the US have seen the first hints of an unusual solid- state phenomenon known as the quantum spin Hall effect Quantum spin Hall state is a topologically non-trivial quantum state, which can be used for Effects of strain and applied electric fields are also discussed. , it is simply a number) and very nearly equal to 1/137. In the research published in Science ("Quantum spin Hall effect of light"), the team found that photons share with electrons a property related to spin—the quantum spin Hall effect. Fazzio1, ‡ 1 Instituto de F´ısica, Universidade de S˜ ao Paulo, CP 66318, 05315-970, S˜ ao Paulo, SP, Brazil. Most quantum states of condensed matter are classified by the symmetries they break. A similar quantized thermal Hall effect is expected in chiral topological superconductors. 1The State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China. 1t-0. Quantum Spin Hall Effect B. Graphene II. Luttinger (1964) considered photons in a grav. We propose an experiment to demon- • Quantum Hall effect 55 Skipping cyclotron orbits Four-terminal sample configuration to measure the Hall and longitudinal resistivities • Quantum Hall effect 56 •For a given plateau not a perfect conductor, ρ xx = 0, ρ xy!= 0 ⇒ electrons move with zero longitudinal resistance. applications in the spin transistors, spin diodes, memories, and so forth. The considerable amount of literature is reviewed. Based on this, we study the quantum spin Hall effect in Bi and Sb in quasi-two and three dimensions using a tight-binding model. In this video, LAURENS MOLENKAMP outlines how his team’s focus on mercury telluride has provided notable insights into this phenomenon. • Spin Hall effect is separation of electron spins perpendicular to current flow • No external magnetic field needed – spin-orbit coupling drives effect • Effect is integral for spintronic devices and topological insulators Color indicates predominant spin composition. Franco Nori . • No external B field is needed. • Natural generalization to D=3, due to spin-orbit force: • 3D hole systems (Murakami et al, Science, PRB) PHYSICAL REVIEW A 82, 053605 (2010) Simulating and detecting the quantum spin Hall effect in the kagome optical lattice. The quantum spin Hall effect has an-other key ingredient: a bulk energy gap. Its conduction and valence bands meet at a point. (Right) The quantum anomalous Hall effect has quantum Hall features without an applied field. We find that these quantum plateaus are robust against the normal dephasing but fragile with the spin dephasing. Siviloglou, Hirokazu Miyake, William Cody Burton, and Wolfgang Ketterle MIT-Harvard Center for Ultracold Atoms, Research Laboratory of Electronics, Department of Physics, The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect-surface modes with strong spin-momentum locking. 2In a normal semiconductor, the same spin-orbit scattering mechanismsare present, and although in this case there is no net charge accumulation, there will be a spin accumulation at opposite edges, giving rise to the so-called spin Hall effect [25]. MIM. The quantum spin Hall effect: Theory and experiment Markus König, Hartmut Buhmann, Laurens W. H0 t cyi cj p VSO cyi dkj dik cj hiji 3 hhijii This class of insulators has been recently found [9,10] to possess a dissipationless quantum spin-Hall effect (QSHE) X y X iVR ci z^ dij cj wi cyi ci ; (1) [11], which is distinct from the intrinsic spin-Hall effect in hiji i the metallic systems [12]. Quantum spin hall effect More recently, a new class of topological states has been both theoretically predicted (Bernevig et al. The Z 2 Very recently, the quantum spin Hall effect in 1T′-WTe 2 MLs at temperatures up 100 K has been reported . The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction respectively. title = "Quantum spin hall effect in inverted type-II semiconductors", abstract = "The quantum spin Hall (QSH) state is a topologically nontrivial state of quantum matter which preserves time-reversal symmetry; it has an energy gap in the bulk, but topologically robust gapless states at the edge. Abanin, Patrick A. Topological phases of matter: from the quantum Hall effect to spin liquids The understanding of collective quantum phenomena in condensed-matter systems has been a central topic in physics, since the beginning of the 20th century and the discovery of superconductivity and superfluidity. The quantum anomalous Hall effect provides spin-polarized dissipation-free transport of electrons, while the quantum spin Hall effect in combination with superconductivity has been proposed as the basis for realizing decoherence-free quantum computing. ELASTIC QUANTUM SPIN HALL EFFECT IN KAGOME … PHYSICAL REVIEW B 98, 094302 (2018) FIG. Jun 25, 2015 · The quantum spin Hall effect is a fundamental property of light. For example, crystalline solids break translational symmetry, and Feb 1, 2018 The quantum spin Hall effect is a unique phase of matter in which the bulk of the material is an insulator, but topological quantum states exist at Jun 26, 2015 It produces a spin-dependent transport of electrons orthogonal to the external driving force (3, 4). Typically, an element possessing high spin-orbit coupling is usually magnetically inactive Nov 25, 2019 · The spin Hall effect was identified some years ago. - Spin orbit induced energy gap in graphene. May 31, 2011 · In a two-dimensional system the quantum spin Hall effect (QSHE) state is characterized by an insulating bulk and two counter-propagating helical edge states. Here 4 is due to the spin and valley degeneracy3 and the 6 signs reflect the electron–hole symmetry. 0 22 0 z xy B hD h ne ve D ve 0 2 D m c eB z h E F If the Fermi energy is between Landau levels, the electron density n is an integer v times the degeneracy of the Landau level n = D0 v z c eB m 0 z hD B e The fractional quantum Hall effect has opened up a new paradigm in the study of strongly correlated electrons and it has been shown that new concepts, such as fractional statistics, anyon, chiral Luttinger liquid and composite particles, are realized in two-dimensional electron systems. 1,2 Tuning spin transport properties is a key step in the spintronic devices but remains quite challenging. Quantum Spin Hall Effect • The QSH state can be thought of as B eff two copies of QH states, one for each spin component, each seeing the opposite magnetic field. "Previously, the spin Hall effect has been observed in Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice Huaqing Huang 1 and Feng Liu 1,2,* 1 Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA Spin Filtered Edge States and Quantum Hall Eﬀect in Graphene Dmitry A. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e)/(4π). Introduction: materials, transport, Hall effects Even higher mobilities result in even more fractional quantum Hall states. Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice Huaqing Huang1 and Feng Liu1,2,* 1Department of Materials Science and Engineering, University of Utah, Salt Lake City, Utah 84112, USA May 21, 2019 · The quantum Hall effect, which is characterized by an insulating bulk and chiral edge states, has recently been generalized from transport of charges to transport of other degrees of freedom, leading to quantum spin Hall and quantum valley Hall effects. Quantum Spin Hall (QSH) has potential applications in low energy consuming spintronic devices and has become a researching hotspot recently. 05t-0. Beeler*, R. 1 This is the first observation of the spin Hall effect in a cold atom system. In an atom, according to the laws of quantum mechanics, electrons move around the nucleus in stationary orbits without losing their energy. Spielman Joint Quantum Institute, National Institute of Standards and Technology and Department of Physics, University of Maryland, Gaithersburg, MD 20899, USA Introduction to spin Hall effect w Jun 26, 2015 · The quantum spin Hall effect is a fundamental property of light In a paper that crystalizes knowledge from a variety of experiments and theoretical developments, scientists from the RIKEN Center for Emergent Matter Science (CEMS) in Japan have demonstrated that the quantum spin Hall effect—an effect known to take place in solid state physics—is also an intrinsic property of light. title = "The quantum spin Hall effect: Theory and experiment", abstract = "The search for topologically non-trivial states of matter has become an important goal for condensed matter physics. This is also known as the quantum anomalous Hall effect. The quantum Hall effect is a quantum-mechanical version of the Hall effect, observed in two-dimensional electron systems subjected to low temperatures and strong magnetic fields, in which the Hall conductance σ undergoes quantum Hall transitions to take on the quantized values Quantum spin Hall effect in HgTe quantum wells. Abstract. When the electron spin is conserved, the integer-quantized ac spin Hall conductivity can be linked to the winding numbers of the reflection matrices in the electrodes, which also equal to the bulk spin Chern numbers of the QSH material. The magnetic force is F m = ev d B where v d is the drift velocity of the charge. 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. Quantum Hall effect exists in D2, due to Lorentz force. (Bernevig and Zhang, PRL, 2006) • The QSH state does not break the time reversal symmetry, and can exist without any external magnetic field. 20 3082–6), are both revealed to exhibit intrinsic 2D/3D quantum anomalous Hall effect with energy gaps up to 36 meV. 00 / 3 votes) Translation Find a translation for Quantum Spin Hall In materials where the spin-orbit interaction is strong, a spin-up electron will be deflected in one direction on encountering a nuclear magnetic field, while a spin-down nucleus will be deflected in the opposite direction - an effect dubbed the quantum spin Hall effect. However, everywhere I look I just find 'the spin-orbit interaction couples the charge and spin current'. Andrei Bernevig Shou-Cheng Zhang 1 Quantum Anomalous Hall Insulators. LeBlanc, A. • Lorentz force and spin-orbit forces are both velocity dependent. Natural generalization to D3, due to spin-orbit force; 3D hole systems (Murakami, Nagaosa and Zhang, Science 2003) 2D electron systems (Sinova et al, PRL 2004) 3. Time-reversal symmetry and fermion parity pumps. Unlike the previous QSHE, this QSHE appears in the absence of spin-orbit interaction and thus, is arrived at from a different physical origin. Basic physics underlying the phenomenon is explained, along with diverse aspects such as the quantum Hall effect as the resistance standard. Fractional quantum Hall effect in a relativistic field theory We construct a class of 2+1 dimensional relativistic quantum field theories which exhibit the Fractional Quantum Hall Effect in the infrared, both in the continuum and on the lattice. 13, 2009) — An international research team has succeeded in gaining an in-depth insight into an unusual phenomenon. J. Jimenez-Garcia, L. We predict a quantum spin Hall effect (QSHE) in ferromagnetic graphene under a magnetic ﬁeld. The fractional quantum Hall effect1–4 (FQHE) in an electron gas with multiple internal degrees of freedom provides a model system to study the interplay between symmetry breaking and emergent topological order5. Seixas,1, ∗ J. 16, 2007 Introduction – Spin Hall effect spin Hall effect in Pt Quantum spin Hall phase 2D 3D phase transition from the ordinary insulator phase Stanford physics Professor Shoucheng Zhang says a new generation of semiconductors, designed around the phenomenon known as the Quantum Spin Hall Effect, could keep Moore’s law in force for decades to come. Perry, I. In stark contrast to its closest kin, the integer quantum Hall state, the QSH state exists only in time‐reversal symmetric system (e. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2e4π. Since its discovery in HgTe/CdTe quantum wells and InAs/GaSb heterostructures, all such systems have so far been suffering from extremely low operating temperatures, rendering any technological application out of reach. SWC Seminar - Topology in Magnets: From classical spin crystals to novel quantum liquids | Shull Wollan Center ABSTRACT Skyrmions are spatially localized topological entities which were proposed in particle physics, and have condensed matter analogues which were discovered in quantum Hall systems and magnetic solids. An effort is made to compromise the flux-attached electron theory with the angular momentum theory which shows that some of the composite fermions become bosons. In the quantum Hall effect, a strong mag-netic field opens a gap as it puts electrons in quantized cyclotron orbits. The Fractional quantum Hall effect I. It involves spin-up electrons conducting along one edge of the insulator, with spin-down electrons conducting along the other side. The fine-structure constant α is of dimension 1 (i. , 2015). We show that this phase is associated with a novel Z 2 topological invariant, which distinguishes it from an ordinary insulator. Apr 11, 2015 · In quantum Hall effect, External huge magnetic field and low temperature are the uttermost requirement but QSH is the special case of quantum hall effect without the application of external magnetic field. Eisenstein Institute for Quantum Information and Matter, Department of Physics, California Institute of Technology, Pasadena, California 91125, USA L. Course on topology in condensed matter 9,878 views Integer quantum Hall effect, which is the Hall effect quantized into integer times e 2 /h (e: elementary charge, h: Planck’s constant) observed in two-dimensional electron gases in strong magnetic fields, is reviewed from both experimental and theoretical standpoints. Chem. Oct 12, 2012 · A quantum spin Hall system possesses a pair of helical edge states. Originally the quantum Hall effect (QHE) was a term coined to describe the unexpected observation of a fundamental electrical resistance, with a value independent of the microscopic details of the semiconductor device. , electron Oct 19, 2018 · The recent observation [1] of a half-integer quantized thermal Hall effect in α -RuCl 3 is interpreted as a unique signature of a chiral spin liquid with a Majorana edge mode. A nontrivial quantum spin Hall effect (QSHE) band gap of 0. Monolayer As-graphane is constituted by using As adsorbing on graphane with honeycomb H vacancies. Liu. In the research published in Science, the team found that photons share with electrons a property related to spin—the quantum spin Hall effect. Here, Spin orbit coupling plays the crucial part and Oct 19, 2017 · The Spin Hall Effect is a transport phenomenon consisting of the appearance of spin accumulation on the lateral surfaces of a sample carrying electric current. These simple binary compounds are also revealed to be ferromagnets with high Curie temperature, which guarantees that the quantum anomalous Hall effect survives at ambient condictions. In a kagome lattice, the time reversal symmetry can be broken by a staggered magnetic flux emerging from ferromagnetic ordering and intrinsic spin-orbit coupling, leading to several well-separated nontrivial Chern bands and intrinsic quantum anomalous Hall effect. It is defined in a lattice Brillouin zone, which enables us to implement numerical calculations for realistic models even in three dimensions. The integer quantum Hall effect is very well understood, and can be simply explained in terms of single-particle orbitals of an electron in a magnetic field (see Landau quantization ). Quantum anomalous Hall-quantum spin Hall effect in optical superlattices. Ce Shang, Xianfeng Chen, Weidong Luo, and Fangwei Ye. So far, a number of theoretical proposals Quantum Spin Hall Effect. • Both carriers go in opposite directions. Williams, K. The spin Hall effect, whereby flowing particles experience orthogonally directed, spin-dependent Lorentz-like forces, is observed in a quantum-degenerate gas and used to produce a cold-atom spin Dec 15, 2006 · We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride–cadmium telluride semiconductor quantum wells. potential ψ (r). Apart from being easy to implement, proven safe and requires no maintenance, it is also the easiest and fastest fix to reducing energy cost. 3,4 Recently, it has been found that two-dimensional topological insulators (2DTI) exhibit quantum spin Hall (QSH) eﬀect with spin- Jun 05, 2013 · The spin Hall effect is seen in electrons and other quantum particles when their motion depends on their magnetic orientation, or "spin. The transverse voltage (Hall effect) measured in a Hall probe has its origin in the magnetic force on a moving charge carrier. However, the small band gap in materials that have been identified as QSH insulators limits applications. In the absence of dephasing, the longitudinal resistance in a QSHE system exhibits the quantum plateaus. Graphene, the Quantum Spin Hall Effect and topological insulators I. Hughes, Shou-Cheng Zhang (Stanford University) Kane and Mele's argument on the existence of edge states in quantum spin Hall effect of graphene. Feb 19, 2018 · I have been trying to understand how the spin hall effect comes about. The spatial proximity of the two lanes leads to backscattering between them, as if the electrons make U-turns. Berry curvature and finite Hall effect in chargeneutral currents- 2. Quite the same Wikipedia. Levitov Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139 Electron edge states in graphene in the Quantum Hall e ﬀect regime can carry both charge and spin. Introduction to Time-reversal symmetry and fermion parity pumps; Adding symmetry to a topological insulator; A perfectly transmitted channel and Kramers Apr 26, 2013 · This phase transition from a two dimensional topological insulator to a trivial insulating state is accompanied by a quenching of the quantum spin Hall effect and the onset of a quantum valley Hall effect, providing a tool to experimentally tune the topological state of silicene. Graphene isn’t ordinarily an insula-tor. In the bulk of the material, there is no net spin. Jul 02, 2015 · This effect is known as the classical spin Hall effect, and quantum mechanics adds a dramatic twist on top. Sun 06 Aug 2017. Guocai Liu, 1Shi-Liang Zhu,2 Shaojian Jiang, 1Fadi Sun, and W. 8 eV was observed experimentally in ML Bi on the top of a SiC substrate 28 . Hughes B. by including a (fictitious) grav. Spin-Dependent Lorentz Force Jun 26, 2015 · The Quantum Spin Hall Effect Is A Fundamental Property Of Light In a paper that crystalizes knowledge from a variety of experiments and theoretical developments, scientists from the RIKEN Center for Emergent Matter Science (CEMS) in Japan have demonstrated that the quantum spin Hall effect—an effect known to take place in solid state physics The quantum spin Hall effect for electrons allows for the existence of an unusual type of material—called a topological insulator—which conducts electricity on the surface but not through the bulk of the material. The quantum spin Hall state is a state of matter proposed to exist in special, two- dimensional, semiconductors that have a quantized spin-Hall conductance and Jan 1, 2010 In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic Jan 7, 2008 In two dimensions the helical edge states give rise to the quantum spin Hall (QSH ) effect, in the absence of any external magnetic field. Real experimental systems, however are far from the idealized picture presented above in which spin-up and spin-down electrons are not coupled. A quantum anomalous Hall effect (QAHE) has been realized in the Cr-doped magnetic topological insulator at an extremely low temperature (∼30 mK). Add to My List Edit this Entry Rate it: (2. Without an external magnetic ﬁeld, spontaneous magnetization combined with spin-orbit coupling gives rise to a quantized Hall conductivity. In two dimensions the helical edge states give rise to the quantum spin Hall (QSH) effect, in the absence of any external magnetic field. These states are known as quantum spin hall (QSH) states. "We were able to show for the first time that two spin currents flow in opposite directions in the edge region of an alloy Simulating and detecting the quantum spin Hall effect in the kagome optical lattice Guocai Liu, 1 Shi-Liang Zhu, 2 Shaojian Jiang, 1 Fadi Sun, and W. This personal review demonstrates that condensed matter physics Jun 26, 2015 · There is also the quantum spin Hall effect (QSHE) (5, 6), which is characterized by unidirectional edge spin transport—edge states with opposite spins propagating in opposite directions. • Better name: Z 2 topological insulator Kane,Mele, 2004 • Graphene (Kane/Mele) Pt : large spin Hall effect Quantum spin Hall effect: • 2D & 3D • Edge states--- topologically protected • Bismuth and surface states spin current • Phase transition between the quantum spin Hall phase and ordinary insulator phase. Just as manipulating electron charge is central Until now, the quantum spin Hall effect could only be indirectly proven. + V V = -eE. Andrei Bernevig Princeton Center for Theoretical Physics Texas A&M, April 2007 With: Taylor L. The group was able to show that the unusual transverse spin they found in evanescent waves was actually caused by the intrinsic quantum Hall effect of photons, and their findings also explain recent experiments that have shown spin-controlled unidirectional propagation of surface optical modes. • A new type of 1D metal: the helical liquid. Just as manipulating electron charge is central quantum Hall effect, and was discovered experimentally in the beginning of the eighties [33]. Quantum Spin Hall Effect • A naïve view: same as before but in an insulator-If spin is conserved, clearly need edge states to transport spin current-Since spin is not conserved in general, the edge states are more fundamental than spin Hall effect. Key advantage ; electric field manipulation, rather than magnetic field. 0 0. . " Previously, the spin Hall effect has been observed in electrons confined to a two-dimensional semiconductor strip, and in photons, but never before in a BEC. Rashba Department of Physics and Center for Nanoscale Systems, Harvard University, Cambridge, Massachusetts 02138, USA The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. Mar 1, 2008 In two dimensions the helical edge states give rise to the quantum spin Hall (QSH ) effect, in the absence of any external magnetic field. After a short overview of what was originally suggested as the quantum spin Hall effect (quantum spin conductance determined by the topological Chern number) the paper analyzes the crucial role of the boundary condition on the observation of the effect and finally discusses whether and how the quantum spin Hall effect could be observed. This novel elec-tronic state with time-reversal invariance is gapped in the bulk and conducts charge and spin in gapless edge states The quantum spin Hall effect and topological insulators Xiao-Liang Qi and Shou-Cheng Zhang In topological insulators, spin–orbit coupling and time-reversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Spin Hall and quantum spin Hall effects Shuichi Murakami Department of Physics, Tokyo Institute of Technology PRESTO, JST YKIS2007 (Kyoto) Nov. Given the existence of one lane, time reversal symmetry mandates the existence of the other. The quantum anomalous Hall effect (QAHE) is a fundamental transport phenomenon in the ﬁeld of condensed-matter physics. The moment you introduce time reversal symmetry $\mathbb{Z}$ collapses to $\mathbb{Z}_2$. W. Just better. It was predicted theoretically and then Fractional quantum Hall effect: Experimental progress and quantum computing applications (Nanowerk News) The Hall effect, discovered in 1879, is observable when a Hall voltage perpendicular to the current is produced across a conductor under a magnetic field. One of the most celebrated topological phases is the quantum spin Hall (QSH) state, that characterises time-reversal-symmetric (TRS) topological insulators in two dimensions (2D), such as HgTe quantum wells or Bismuth-based compounds [11–14]. 05. • Quantum SHE. Quantum Spin Hall Effect. The quantum spin Hall effect and topological insulators. An interesting alternative is to have the The influence of dephasing on the quantum spin Hall effect (QSHE) is studied. The materials which exhibit quantum Hall effect such as graphene, are like atoms, The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Recently, a new class of topological insulators has been proposed. Thermal Hall Effect from Neutral Currents in Quantum Magnets 1. In this article, we review the theoretical foundations and experimental discovery of the quantum spin Hall effect. 5 G z sH (e/8 π) Rashba SO coupling Q R E F =-0. Quantum Anomalous Hall Effect (QAHE ®) coating is a revolutionary solution for energy saving. Quantum Spin Hall Effect Without Landau Levels, (non-magnetic semiconductors with Spin-Orbit coupling) Graphene, Topological Semicond by correlating the Haldane model with spin (Kane and Mele, PRL (2005), Qi, Wu, Zhang PRB (2006)); With Landau Levels correlated with spin through SO coupling (Bernevig and Zhang, PRL (2006)); • (Sheng et al, PRL, (2005); Mar 10, 2011 · The Quantum Spin Hall Effect For example, crystalline solids break translational symmetry, and ferromagnets break rotational symmetry. Any help would be much appreciated Jun 13, 2013 · Such spin-Hall effects have been observed for electrons ﬂowing in materials such as GaAs or InGaAs [5, 6]; for laser light traversing dielectric junctions [7]; and now for the ﬁrst time in quantum gases moving through an optical ﬁeld. Photonic spin Hall effect (SHE) manifesting itself as spin-dependent splitting escapes detection in previous photon tunneling experiments due to the fact that the induced beam centroid shift is restricted to a fraction of wavelength. Hall Voltage for Positive Charge Carriers. Spin Hall effect The spin Hall effect is the creation of a spin imbalance, or spin current, due to scattering of electron spin moments in a direction perpendicular to an applied electric field. the Hall plateau) as the electron density is varied. Appendix: “Quantum ”Spin Hall Effect in Rings 0 2 4 6 8 10-0. 31 Annu. Topological gapless phase in 3D Spin Hall effect in metals and semiconductors k E The Quantum Spin Hall E ect in HgTe/CdTe Quantum Wells D. Pfeiffer and K. DkDyakonov &VI& V. C. , 2006; Haldane, 1988; Kane and Mele, 2005), and also experimentally observed (Konig et al. . Have a question? . The QAHE Quantum spin Hall effect on germanene nanoroad embedded in a completely hydrogenated germanene L. The Quantum Hall effect is explained on the basis of angular momentum theory. Jun 25, 2015 · The quantum spin Hall effect for electrons allows for the existence of an unusual type of material—called a topological insulator—which conducts electricity on the surface but not through the 2007 of the so-called quantum spin Hall effect in HgTe quantum wells, a new topological state of quantum matter. Molenkamp et al,. 5 0. Apr 07, 2015 · Quantum Hall effect intro (by Ady Stern) - Duration: 8:00. Furthermore, the residual conductance is destroyed by a small external magnetic field. Jan 31, 2013 · Furthermore, the gapless edge states are spin-filtered and are insensitive to the non-magnetic disorder. A very important achievement was the realization that the quantum spin Hall state is robust to the introduction of spin-up spin-down scattering. Oct 12, 2012 · Abstract. Sep 08, 2011 · Quantum spin Hall effect in 2D topological insulators Sonin, E. To install click the Add extension button. The system possesses a variety of quantum phase transitions over a large parametric space and two important topological phases, namely, quantum anomalous Hall (QAH) and quantum spin Hall (QSH) phases are found to coexist in the system, but they reside in different bandgaps. Here, we predict existence of quantum spin Hall effects and tunable spin transport in As-graphane, based on first-principle density functional theory and tight binding calculations. Graphene. Three Dimensional Generalization - Topological Insulator, Surface States The quantum Hall effect is referred to as the integer or fractional quantum Hall effect depending on whether ν is an integer or fraction, respectively. Home Courses Topology in Condensed Matter Subjects 05. Quantum Spin Hall Effect And Topological Phase Transition in HgTe Quantum Wells B. From first-principles, we predict that QAHE can also be achieved in a well-designed graphene nanomesh without the requirement of transition metal doping. Based on this line of reasoning, it was shown (6) that the intrinsic spin Hall effect can in principle exist in band insulators, where the spin current can flow without dissipation. I. EPS Europhysics Prize (968 words) exact match in snippet view article find links to article Theoretical prediction and the experimental observation of the quantum spin Hall effect and topological insulators 2008: Andre Geim and Kostya Novoselov ScienceDaily (Feb. Although the Hall effect was discovered in a sheet of gold leaf by Edwin Hall, this Shortly after discovery of the integer quantum Hall effect (IQHE) in two dimensional electron system (2DEG) upon strong magnetic fields corresponding to complete fillings of succeeding Landau levels (LLs), the surpris-ing observation of the fractional quantum Hall effect (FQHE) was reported at stronger magnetic fields resulting Current advances: The fine-structure constant and quantum Hall effect . In this work, we show that when the HgTe QW are doped with magnetic Mn atoms, the QAH effect can be realized within an experimentally accessible parameter regime. Feb 19, 2012 · Thus the nonzero spin accumulation persists only for the QSH phase, justifying the term quantum (but not quantized) spin Hall effect. only to the integer quantum Hall effect), after threading a flux quantum the Hamiltonian is the same, but the state has changed into an excited state. Pan,et al. In the quan-tum spin Hall effect, the gap is always there: The effect occurs in insulators. quantum spin hall effect