Christiansen et al photonic topological insulators with quantumspinhall edge states upon suitable lattice perturbations, may be gapped in a topological nontrivial way. Topological phase transition and quantum spin hall edge. Superconducting proximity effect, majorana fermions. When the spinorbit coupling soc is strong enough to invert the conduction and valence bands in the material,,,, it creates a new state of matter, known as the timereversalinvariant z 2 topological insulators tis. Zhang is a professor of physics at stanford university in stanford, california. Video abstract for the article quantum spin hall effect in ivvi topological crystalline insulators by s safaei, m galicka, p kacman and r buczko s safaei et al 2015 new j. It is referred to as integer quantum hall effect as. The quantum hall state is the first, and so far the only example, of a topologically nontrivial state of matter, where the quantization of the hall conductance is protected by a topological invariant.
We propose a new class of semiconductor systems based on multilayer brokengap quantum wells, in which the qshi gap reaches 60 mev and remains insensitive to temperature. Quantum spin hall effect and topological insulators for light. Quantum hall effect and topological insulators joint. Hightemperature quantum anomalous hall effect in n p. To study this phenomenon, scientists apply a large magnetic field to a 2d sheet semiconductor.
Pdf quantum spin hall effect in 2d topological insulators. We envision that the quantum spin hall effect should be observed in 111oriented thin films of snse and snte topological crystalline insulators. Therefore if a material is in the topological insulator state they frequently call it the quantum spin hall state. The quantum spin hall effect and topological insulators xiaoliang qi and shoucheng zhang in topological insulators, spinorbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Quantum spin hall effect and topological insulators for light konstantin y. In 3d, magnetic order opens up a gap for the topological surface states, and chiral edge state has been predicted to exist on the magnetic domain walls. Qsh was the first example of a quantum state with spontaneously broken symmetry, meaning it comprises of a symmetric probability distribution where any pair of outcomes has the same probability of occurring. While the anomalous hall effect requires a combination of magnetic polarization and spinorbit coupling to generate a finite hall voltage even in the absence of an external magnetic field hence called anomalous, the quantum anomalous hall effect is its. Quantum spin hall effect in iv vi topological crystalline. Topological insulators tis, which exist in two and three dimensions, represent a new electronic phase stemming from the topological character of the bulk wave functions of certain materials and compounds. Pdf the quantum spin hall effect and topological insulators. We show that freespace light has intrinsic quantum spinhall effect qshe properties. The twodimensional topological insulator mercury telluride can be described by an effective hamiltonian that is essentially a taylor expansion in the wave vector k of the interactions between the lowest. The search for room temperature quantum spin hall insulators qshis based on widely available materials and a controlled manufacturing process is one of the major challenges of todays topological physics.
In 2d topological insulators, magnetic order breaks the symmetry between the counterpropagating helical edge states, and as a result, the quantum spin hall effect can evolve into the qah effect. Recently, a new class of topological states has emerged, called quantum spin hall qsh states or topological insulators see physics today, january 2008, page 19. After that i will describe the kane and mele model 11 for the quantum spin hall e ect in graphene and discuss its relation to a general quantum spin hall system. Quantum anomalous hall effect is the quantum version of the anomalous hall effect. Quantum hall effect and edge channels with a nonquantized term m. This causes a gap to open between energy bands, and. For a video introduction of topological insulators, see this url. When the thickness of the quantum well is varied, the electronic state changes from a normal to an inverted type at a critical thickness d c. The quantum anomalous hall effect qahe is a quantized hall effect that occurs at zero magnetic field. Therefore, the surface state of a weak topological insulator with translation symmetry breaking on the surface has a half quantum spin hall effect, in the same way that the surface state of a strong topological insulator with timereversal symmetry breaking. Quantum spin hall effect and their topological design of.
From the quantum hall effect to topological insulators. Topological insulators topological insulator surface states experiment. Zhang,6 xiaohong xu,2, and zhenyu zhang1, 1international center for quantum design of functional materials icqd, hefei national laboratory for physical sciences at. The search for topological states of matter that do not require magnetic fields for their observation led to the theoretical prediction in 2006 and experimental observation in 2007 of the socalled quantum spin hall effect in hgte quantum wells, a new topological state of quantum matter. These are characterized by a nonzero topological spin chern number. 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 telluridecadmium telluride semiconductor quantum wells. Mele department of physics and astronomy, university of pennsylvania, philadelphia, pennsylvania 19104, usa received 26 july 2006. Designing photonic topological insulators with quantum. Cubuk,4 hua chen,5 wenguang zhu,1,3 efthimios kaxiras,4 s. The joint quantum institute is a research partnership between university of maryland umd and the national institute of standards and technology, with the support and participation of the laboratory for physical sciences. The quantum hall effect qhe is one of the most striking phenomena in the field of condensed matter physics since its discovery in the 1980s 1. Its mechanism and properties are different from those of conventional quantum hall effects qhes induced by magnetic field. They are also called quantum spin hall systems, because they are the gapped analogues of spin hall systems, just as the quantum hall effect is to the hall effect.
The quantum spin hall state is a state of matter proposed to exist in special, twodimensional, semiconductors that have a quantized spinhall conductance and a vanishing chargehall conductance. Then i will present laughlins original model 16 for the quantum hall e ect and brie y discuss its limitations. Bliokh1,2 and franco nori1,3 1 center for emergent matter science, riken, wakoshi, japan. Quantum anomalous hall effect in magnetic topological. Tomonagaluttinger liquid in the edge channels of a. To overcome the limitations imposed by the low spin orbit. 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. Physics the quantum hall effect gets more practical. Such topological states with spin momentum locking gave rise to a new class of materials. In topological insulators, spinorbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Hightemperature quantum anomalous hall effect in np codoped topological insulators shifei qi,1,2 zhenhua qiao,1,3 xinzhou deng,1,3 ekin d. Graphene and the quantum spin hall effect penn physics.
Hinged quantum spin hall effect in antiferromagnetic topological insulators. The quantum spin hall effect and topological insulators xiaoliang qi is a research associate at the stanford institute for materials and energy science and shoucheng zhang is a professor of physics at stanford university in stanford, california. Quantum spin hall systems and topological insulators. Topological insulators and the quantum spin hall effect. The first theory of a qhe without a magnetic field was proposed in 1988. Hinged quantum spin hall effect in antiferromagnetic topological. Using a tightbinding approach supported by firstprinciples calculations of the band structures we demonstrate that in these films the energy gaps in the twodimensional band spectrum depend in an oscillatory fashion on the layer thickness. Topological insulators in three dimensions liang fu, c. Quantum spin hall insulators are twodimensional materials that host conducting helical electron states strictly confined to the onedimensional boundaries. Topological insulators and applications to quantum.
Quantum spin hall effect time reversal symmetry and edge states experiment. Topological insulators are insulating in the bulk but have gapless edgesurface states, which carry a pure spin current. Half quantum spin hall effect on the surface of weak. Magnetic topological insulators and quantum anomalous hall.
The discovery of the integer quantum hall effect in twodimensional electron gas opens a window to explore topological phases in quantum matter 1,2. To overcome the limitations imposed by the low spinorbit. The quantum spin hall state of matter is the cousin of the integer quantum hall state, and that does not require the application of a large magnetic field. Topological insulators can be realised in both two dimensions 2d and in three dimensions 3d, and are nonmagnetic insulators in the bulk that possess gapless edge. The essence of the quantum spin hall effect in real materials can be captured in explicit models that are particularly simple to solve. It is known that the integer v is the topological invariant of. Quantum spin hall effect and topological insulators nanotec. Topologically distinct from all other known states of matter, including qh states, qsh states have been theoretically predicted and experimentally observed in mercury telluride quantum wells, 2,3 2. Quantum spin hall effect in ivvi topological crystalline. Topological insulators could bring future computing platforms based on spintronics. Quantum spin hall effect and topological insulators for light arxiv. Largegap quantum spin hall insulators in tin films yong xu,1,2 binghai yan,3 haijun zhang,1 jing wang,1 gang xu,1 peizhe tang,2 wenhui duan,2 and shoucheng zhang1,2, 1department of physics, mccullough building, stanford university, stanford, california 943054045, usa 2institute for advanced study, tsinghua university, beijing 84, peoples republic of china. A superconducting quantum hall system is predicted to be a chiral topological superconductor, which can be used to realize topological quantum computinga quantum computing approach that is naturally robust against quantum decoherence.
Therefore if a material is in the topological insulator state they. The original motivation of great interest to topological insulators was the hope to observe the quantum spin hall effect. The story of the topological insulator began with the discovery of the quantum spin hall effect qsh in 1980. But the large field needed for the quantum hall effect would destroy most superconducting states. Quantum spin hall insulator with a large bandgap, dirac. The time reversal symmetry breaking on the surface can be realized by ising type magnetic moments oriented along the surface normal. Conventional computers use the presence and absence of electric charges to. Quantum spin hall effect and topological phase transition. Fritz1 1 institute for theoretical physics, university of cologne, cologne, germany department of condensed matter physics, the weizmann institute of science, 76100 rehovot, israel received 12. Using a tightbinding approach supported by firstprinciples calculations of the band structures, we demonstrate that in these films the energy gaps in the twodimensional band spectrum depend in an oscillatory fashion on the layer thickness. This robustness stems from the topological nature characterized by the z 2 topological number, and this offers us various kinds of new novel properties.
Notably, all dielectric pcbased quantumspinhall pti designs to date employ the. 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. The quantum anomalous hall qah effect, which has been realized in magnetic topological insulators tis, is the key to applications of dissipationless quantum hall edge states in electronic devices. Such topological states with spinmomentum locking gave rise to a. Topological insulators quantum spin hall systems are insulating in the bulk but have gapless edgesurface states, which remain gapless even when nonmagnetic disorder or interaction is present. Quantum spin hall effect in topological insulators. Valley polarized quantum hall effect and topological.
Bernevig and zhang, prl, 2006 the qsh state does not break the time reversal symmetry, and can exist without any external magnetic field. In topological insulators, spin orbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Topological insulators display unique properties, such as the quantum spin hall effect, because timereversal symmetry allows charges and spins to propagate along the edge or surface of the. The quantum spin hall effect and topological insulators xiaoliang qi and shoucheng zhang in topological insulators, spin orbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. Keywords quantum spin hall effect, spintronic devices, topological insulators. Edge states and integer quantum hall effect in topological. The quantum hall effect, a quantum phenomenon that appears in macroscopic length scale, is one of the most important topics in con quantum anomalous hall effect in magnetic topological insulators ieee conference publication. Quantum spin hall effect and topological insulators. In the quantum hall effect the longitudinal conductance vanishes while the hall conductance. We envision that quantum spin hall effect should be observed in 111oriented thin films of snse and snte topological crystalline insulators. Pdf quantum spin hall effect and topological insulators.
Quantum spin hall effect in 2d topological insulators. Yet, it has taken 25 years to be experimentally realized, which has now happened thanks to the. Enhancing the quantum anomalous hall effect by magnetic. While twodimensional 2d topological insulators tis initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin. Quantum spin hall effect and topological phase transition in hgte quantum wells. The half quantum hall effect is responsible for the topological magnetoelectric effect of the strong ti. Voltage drop is measured to see whether the conductance becomes zero or not. Inspired by the fractional quantum hall effect, spin liquids, and fractional chern insulators, we develop a wave function approach to a new class of topological order in a twodimensional crystal. 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.
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