Roy r 2009 topological phases and the quantum spin hall effect in three dimensions phys. The quantum spin hall effect theory and experiment pdf download. Compendium of quantum physics concepts, experiments. 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. Observation of the quantum spin hall effect up to 100. There are surprisingly few dedicated books on the quantum hall effect. Quantum spin hall insulators are twodimensional materials that host conducting helical electron states strictly confined to the onedimensional boundaries.
Bernevig and zhang, prl, 2006 the qsh state does not break the time reversal symmetry, and can exist without any external magnetic field. Experimental signatures of the qsh effect have recently been reported in an atomically thin material, monolayer wte2. The quantum anomalous hall effect is a novel manifestation of topological structure in manyelectron systems and may have potential applications in future electronic devices. Realization of the quantum spin hall effect in graphene devices has remained an outstanding challenge dating back to the inception of the field of topological insulators. Since its inception in the early part of the twentieth century, quantum physics has fascinated the academic world, its students, and even the general public. The quantum hall effect graduate texts in contemporary. Quantum hall effects an introduction 1 quantum hall effects an introduction m. In this experiment, a semiconductorheterostructure with a twodimensional. Quantum spin hall systems and topological insulators. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from ntype to ptype, passing through an. Z2 topological order and the quantum spin hall effect. L w, hughes t, liu c x, qi x l and zhang s c 2008 the quantum spin hall effect. The quantum spin hall effect is a fundamental property of. Quantum spin hall systems and topological insulators iopscience.
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. What conductance is measured for the quantum spin hall. Readers are referred to chapter 4 for the basic concepts of quantum hall effects in semiconductors, e. I think that what the authors are trying to do is emphasize the difference between the quantized spin hall effect and the quantum spin hall effect. In order experiment was introduced a topological z 2, invariant who characterizes a state as trivial or. Many new research fields are based on quantum hall physics, and some of them are covered by separate overviews in this journal, such as composite fermion theory of exotic fractional qhe, exciton condensation in bilayer quantum hall systems, the quantum spin hall effect, and quantum anomalous hall effect. Graphenes exceptionally weak spinorbit couplingstemming from carbons low massposes the primary obstacle. Quantum hall effects in graphene 55, 56 have been studied intensively. One of the best known examples is the berry phase m. The existence of the quantum hall effect requires breaking of the time reversal symmetry caused by an external magnetic. Assume the conductor to have charge carrier of charge q can be either positive or negative. 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. Maxwells equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. Furthermore, in experiment, the fermi energy can be tuned by the application of a.
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. In the presence of a strong magnetic field, charged particles confined to move in the plane can form a series of new states of matter with bizarre properties. Ppt quantum hall effects an introduction powerpoint. In fact, it is or has become a highly interdisciplinary eld. 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. Two prominent ones are prange and girvin, \the quantum hall e ect this is a collection of articles by most of the main players circa 1990. The latter ones result in remarkable geometric and topological phenomena related to the spin1 massless nature of photons. Theory and experiment the search for topologically nontrivial states of matter has become an important goal for. Theory and experiment by markus koenig, hartmut buhmann, laurens w. 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. We experimentally and theoretically study artificially enhanced spinorbit coupling in graphene via.
These kinds of sensors with typical dimensions of the sensitive element of 0. Polarization represents a twodimensional quantum system, so the introduction to quantum mechanics uses twodimensional state vectors and operators. On a topic such as the physicsof the atom the disciplines of physics. Plotting the hall resistance essentially the reciprocal of the hall conductance of a lowtemperature twodimensional electron gas against the strength of the imposed magnetic field normal to the gas plane, one finds a stairlike quantized sequence of hall conductances very precisely equal to ne 2 h, where n is the integer that characterizes each. Xiao gang wen, quantum field theory of manybody systems. The hall effect was discovered in 1879 by edwin herbert hall while working on his doctoral degree at the johns hopkins university in baltimore, maryland, usa discovered 18. Provides new physics and new devices previously published work. But in a 2006 theory paper, zhang and two of his students, andrei. The quantum anomalous hall effect is defined as a quantized hall effect realized in a system without an external magnetic field.
In this work,we predict a quantized spin hall effect in. As i will describe shortly, quantized spin hall effect is not possible. So far the applicability and measurements of the berry phase were mostly limited. Geometric phases in quantum mechanics play an extraordinary role in broadening our understanding of fundamental significance of geometry in nature. There are surprisingly few dedicated books on the quantum hall e ect. To do so we will use the drude theory of conductors. Hughes, chaoxing liu, xiaoliang qi and shoucheng zhang no static citation data no static citation data cite.
Please do email me if you find any typos or mistakes. For example, say you are trying to observe the spin analogue of the integer quantum hall effect. The basic experiment, shown in figure 2, features a hall bar of length. Quantum hall effect an overview sciencedirect topics. Tomonagaluttinger liquid in the edge channels of a. Landau levels, cyclotron frequency, degeneracy strength, flux quantum, compressibility, shubnikovde haas. The search for topologically nontrivial states of matter has become an important goal for condensed matter physics. Quantum spin hall effect shows up in a quantum well insulator, just.
The quantum hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. 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. Theory of large intrinsic spin hall effect in iridate semimetals nature. Quantum parity hall effect in bernalstacked trilayer graphene. We compare our findings with the recent experimental report on the discovery of large spin hall effect in sriro3 thin films. A quantum spin hall system possesses a pair of helical edge states. Theory and experiment markus konig1, hartmut buhmann1, laurens w. Recent theory predicted that the quantum spin hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in hgtehg,cdte quantum wells. Hughes, chaoxing liu, xiaoliang qi, shoucheng zhang download pdf. This voltage is a direct measure of the magnetic field as long as the current is constant. Mele department of physics and astronomy, university of pennsylvania, philadelphia, pennsylvania 19104, usa received 22 june 2005.
The basics are described well but theres nothing about chernsimons theories or the importance of the edge modes. Hall effect sensors are based on a thin film of semiconducting material typically indium arsenide in which a voltage perpendicular to an applied current and an applied magnetic field appears fig. Xiaogang wen, quantum field theory of manybody systems. The quantum hall effect is a quantummechanical version of the hall effect, observed in. Harsh shukla hall sensor hall effect and its applications hall effect thruster 2. 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. The key ingredient in both the intrinsic and quantum spin hall effects is spinorbit coupling.
Hall effect experiment utk department of physics and. Energy of the first 12 spinsplit landaulevels as a function of the mag. The quantum spin hall phase shares many similarities with the quantum hall effect. Dynamical quantum hall effect in the parameter space pnas. Why this paper is important importance of quantum spin hall effect.
Here, we report a class of quantum hall effect, the quantum parity hall qph effect, in which boundary channels are distinguished by even or. Furthermore, because the laboratories involve studying photons, using photon polarization as a prototypical quantum system allows the laboratory work to be closely integrated with the coursework. Here, we directly image the local conductivity of monolayer wte2 using microwave impedance microscopy. Work supported in part by us department of energy contract deac0276sf00515. There is an experiment which exhibits the berry phase in the aharonovbohm effect. Theory and experiment the search for topologically nontrivial states of matter has become an important goal for condensed matter physics. Fortunately, our understanding of this menagerie is based almost entirely on many body wavefunctions of a rather simple form.
Quantum spin hall effect and topological phase transition. What the previously proposed real world examples are. In two dimensions the helical edge states give rise to the quantum spin hall qsh effect, in the absence of any external magnetic field. Quantum spin hall effect and their topological design of.
He discovered, in essence, that the hall conductance, as a function of the strength of the magnetic field applied normal to the gas. Hall effect and quantum spin hall effect arise in the context of lattice gauge theory. View the table of contents for this issue, or go to the journal homepage for more. Topological insulators are insulating in the bulk but have gapless edgesurface states, which carry a pure spin current. The sh effect can be thought of as the spin counterpart to the classical charge hall effect. Why those proposed real world examples are unrealistic importance of this paper. A twodimensional 2d topological insulator exhibits the quantum spin hall qsh effect, in which topologically protected conducting channels exist at the sample edges. The drude theory and the hall effect before considering the effect of magnetic fields on conductors, we need some model to describe the flow of currents in response to electric fields. This is a simple classical model, and many of its concepts extend to. A timereversal tr invariant topological insulator ti in two dimensions, also known as a quantum spin hall qsh insulator, can be identified by its helical edge modes 14. 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. In recent years, the quantum anomalous hall effect was proposed theoretically and realized.