When a qh region is contacted by two superconducting electrodes, the gapped qh bulk prevents the flow of a supercurrent 511. 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. The quantum spin hall effect and topological insulators. Quantum spin hall qsh effect materials feature edge states that are topologically protected from backscattering.
The nature of this plateau is still a matter of debate, and active current research. Quantum spin hall effect and topological phase transition in hgte quantum wells. If you have a 2d confined electron system at very low temperature below the fermi state and affected by a strong magnetic field 10 t. This paper fills the missing piece giving a real world. Observation of unconventional quantum spin textures in. Pdf quantum spin hall effect george rajna academia. The quantum hall effect or integer quantum hall effect is a quantummechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance. In topological insulators, spinorbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical. This is also known as the quantum anomalous hall effect.
While spin hall and quantum spin hall effect are both based on the fact that due to intrinsic spin orbit interaction particles with spin up and spin down, respectively, moving in the same. Quantum spin hall effect and topological phase transition. Pdf spin hall effects are a collection of relativistic spinorbit coupling phenomena in which electrical currents can generate. Revealing topological superconductivity in extended quantum. This conductance is made up of equal contrib utions from opposite edges of the bar, in which the electrons have opposite spin. The quantum spin hall effect is a fundamental property of. Z 2 topological insulator kane,mele, 2004 graphene kanemele. Revealing topological superconductivity in extended quantum spin hall josephson junctions shuping lee,1 karen michaeli,2 jason alicea,1 and amir yacoby3 1department of physics and institute for quantum information and matter, california institute of technology. Existence of the quantum hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. Quantum spin hall effect in two dimensional transition. Voltage drop is measured to see whether the conductance becomes zero or not. Revealing topological superconductivity in extended.
All of them have their genesis in the quantum hall e. In topological insulators, spinorbit coupling and timereversal symmetry combine to form a. It is unusual for a puretheory physics paper to make it into the journal science. The first proposal for the existence of a quantum spin hall state was developed by charles kane and gene mele who adapted an earlier model for graphene by f. In a twodimensional system the quantum spin hall effect qshe state is characterized by an insulating bulk. The spin hall effect is a phenomenon in which, in the absence of a magnetic field, particles such as electrons experience a lorentzlike force with a direction depending on each particles spin. Exotic spin transport phenomena, such as the dissipationless quantum spin hall effect, have been speculated to originate from a topological order whose identification requires a spin sensitive.
The quantum hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Quantum spin hall effect and topological phase transition in. Heuristically this is sort of like a hybrid between spin and charge hall effects. Topological modes at an extended boundary are propagating, but this is not generic. 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. A model for a fractionalized quantum spin hall effect. 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 2collaborative innovation center of quantum matter, beijing 84, china received 15 june 2018. The integer and fractional quantum hall effects were the first topo logical states to be. A generic theory of the integer quantum hall effect yu shen a dissertation presented to the faculty of princeton university in candidacy for the degree of doctor of philosophy recommended for acceptance by the department of physics adviser. The spinorbit coupling thus leads to an accumulation of electrons with different spins on opposite sides of the sample.
What the previously proposed real world examples are. Left the quantum hall effect qhe occurs in a twodimensional electron system under a large applied magnetic field. In topological insulators, spinorbit coupling and timereversal symmetry combine to form a novel state of matter predicted to have exotic physical properties. 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 the edges carrying up spins and down spins. The quantum hall effect can be explained through gauge invariance. Andrei bernevig and shoucheng zhang prl 96, 106802 2006 zhang yu department of physics fudan university.
Quantum anomalous hall effect and quantum spin hall effect. Quantized hall plateaus have been found corresponding to a few even denominator fractions. Spatial separation is at the heart of both the quantum hall qh and the quantum spin hall qsh effects. However, the small band gap in materials that have been identified as qsh insulators limits applications. Bernevig and zhang, prl, 2006 the qsh state does not break the time reversal symmetry, and can exist without any external magnetic field.
Underlying all of these phenomena is an impressive theoretical edi. Exotic spintransport phenomena, such as the dissipationless quantum spin hall effect, have been speculated to originate from a topological order whose identification requires a spinsensitive. Upon threading of quantized magnetic flux through the conven tional system spin s 1 is transferred between the edges, while in the. Why those proposed real world examples are unrealistic importance of this paper. What conductance is measured for the quantum spin hall state. Petr kratochvilpublic domain in a paper that crystalizes knowledge from a. The quantum spin hall qsh effect is a new quantum state of matter, which originates from spin orbit coupling soc and has attracted much attention in recent years because of its fundamental. The quantum spin hall effect is a fundamental property of light. To further investigate the change of the oscillation periodicity, a higher magnetic field up to 18 t was applied as shown in fig. The quantummechanical wave nature of the travelling electrons organises them into neat. We use firstprinciples calculations to predict a class of largegap qsh. Exotic spintransport phenomena, such as the dissipationless quantum spin hall effect, have been speculated to originate from a topological order whose identification. Quantum spin hall effect figure from science 301, 48 2003 the number of edge channels in the sample is directly related to the value of the quantum hall conductance figure from physics today feb 2010. The proposal by bernevig and zhang is based on the spinorbit interaction induced by strain in semiconductors.
A generic theory of the integer quantum hall effect. References home university of waterloo university of. What conductance is measured for the quantum spin hall. Right the quantum anomalous hall effect has quantum hall features without an applied field.
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. The proposal by kane and mele is based on the spinorbit interaction of graphene and is mathematically motivated by the earlier work of haldane 21 on the socalled quantum anomalous hall effect qah effect. This book is a compilation of major reprint articles on one of the most intriguing phenomena in modern physics. Pdf the quantum spin hall effect and topological insulators. This is the starting point for the definition of the z2 invariant 22, 23, 3740. Feb, 2009 a topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetrybased classification of condensed matter. Quantum spin hall effect is a spin version of quantum hall effect. The existence of the quantum hall effect requires breaking of the. Stanford university with andrei bernevig, taylor hughes. 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. What is an intuitive explanation of the quantum hall effect. Phenomenology of the quantum spin hall effect one key element that was instrumental in arriving at the theoretical prediction of the qsh state is the prediction of the intrinsic spin hall sh effect in doped semiconductors 15, 16. Quantum hall effect 55 skipping cyclotron orbits fourterminal sample configuration to measure the hall and longitudinal resistivities quantum hall effect 56 for a given plateau not a perfect conductor. It is also called twodimensional topological insulator.
Together with a detailed introduction by the editor, this volume serves as a stimulating and valuable reference for students and research workers in condensed matter physics and for those with a particle physics background. The quantum spin hall effect goteborgs universitet. But note that time reversal symmetry is broken in such a system. The quantum hall effect is a set of phenomena observed at low temperature in a twodimensional electron gas subject to a strong perpendicular magnetic field. A quantum spin hall system possesses a pair of helical edge states, in which an electric current can induce a transverse spin current or a spin accumulation near the system boundary. A generic theory of the integer quantum hall effect yu shen a dissertation presented to the faculty of princeton university. The quantum spin hall effect is a fundamental property of light 25 june 2015 credit. View the table of contents for this issue, or go to the journal homepage for more. In this work, we predict a quantized spin hall effect in the absence of any magnetic field, where the intrinsic spin hall. The quantum spin hall phase shares many similarities with the quantum hall effect. Timereversalbreaking induced quantum spin hall effect.
Jun 25, 2015 the quantum spin hall effect for electrons allows for the existence of an unusual type of materialcalled a topological insulatorwhich conducts electricity on the surface but not through the. The sh effect can be thought of as the spin counterpart to the classical charge hall effect. Motivated by this suggestion, the quantum spin hall qsh effect has been proposed independently both for graphene 7 and semiconductors 8,9, where the spin current is carried entirely by the helical edge states in two dimensional samples. The interplay of the quantum hall qh effect with superconductivity is expected to result in excitations with nontrivial braiding statistics such as majorana fermions and nonabelian majorana anyons 14. Experimental realization of qsh figure from science 318, 766 2007. While the theory shows that surface states merge with the bulk valence bands. The quantum spin hall state is a state of matter proposed to exist in special, twodimensional, semiconductors that have a quantized spin hall conductance and a vanishing charge hall conductance. Levitov department of physics, massachusetts institute of technology, 77 massachusetts ave, cambridge, ma 029 electron edge states in graphene in the quantum hall e. Revealing topological superconductivity in extended quantum spin hall josephson junctions shuping lee,1 karen michaeli,2 jason alicea,1 and amir yacoby3 1department of physics and institute for quantum information and matter, california institute of technology, pasadena, california 91125, usa 2department of condensed matter physics, weizmann institute of. The classical hall voltage current flow pattern in a hall bar how to solve discovery of the quantum hall the role of mobility the 2deg in a mosfet setting up the quantum mechanical hamiltonian effective masses etc oscillation of the fermi level, landau levels group velocity of the eigenstates channels from a contact to another.
Haldane which exhibits an integer quantum hall effect. Quantum spin hall effect in a twoorbital model on a honeycomb lattice. Evolution of weyl orbit and quantum hall effect in dirac. May 20, 2016 the interplay of the quantum hall qh effect with superconductivity is expected to result in excitations with nontrivial braiding statistics such as majorana fermions and nonabelian majorana anyons 14. Request pdf a fractionalized quantum spin hall effect effects of electron correlations on a two dimensional quantum spin hall qsh system are studied. A fractionalized quantum spin hall effect request pdf. Physics the quantum hall effect gets more practical.
The inverted s and plike band structure of a 2d ti mat. Soon after the theoretical prediction of the intrinsic spin hall e. While spin hall and quantum spin hall effect are both based on the fact that due to intrinsic spinorbit interaction particles with spin up and spin down, respectively, moving in the same. Spurious and realistic solutions for the quantum spin hall.
A topologically ordered material is characterized by a rare quantum organization of electrons that evades the conventional spontaneously broken symmetrybased classification of condensed matter. Aug 19, 2017 quantum spin hall effect is a spin version of quantum hall effect. The quantum spin hall effect for electrons allows for the existence of an unusual type of materialcalled a topological insulatorwhich conducts. The kane and mele model is two copies of the haldane model such that the spin up electron exhibits a chiral integer quantum hall effect. The quantum spin hall qsh effect is a new quantum state of matter, which originates from spinorbit coupling soc and has attracted much attention in recent years because of its fundamental. Graphene quantum hall effect in high magnetic fields as the magnetic field grows, the ll spectrum assumed in eq. Andrei bernevig and shoucheng zhang department of physics, stanford university, stanford, california 94305, usa received 18 april 2005. This effect is known as the classical spin hall effect, and quantum mechanics adds a dramatic twist on top. Why this paper is important importance of quantum spin hall effect.
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