quantum hall state of matter

The circulating edge states of the quantum Hall state are different from ordinary states of matter because they persist even in the presence of impurities. A quantum spin Hall state is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. HgTe, HgSe, HgS, alpha-Sn. The model reproduces the surface structure of Bi1-xSbx and the authors can determine which surfaces will behave as topological metals. In two-dimensional k-space, the dispersion relation looks like two cones that meet at discrete (Dirac) points at the Fermi level. Public users can however freely search the site and view the abstracts and keywords for each book and chapter. Since 1993 he has been a Professor of Physics at Stanford University. for the examples above. When we think of topology, we normally think of objects that cannot be simply transformed into each other, such as a rubber band and a Möbius strip (top). M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang. One of the most striking predictions of topological field theory is the so-called topological magnetoelectric effect, where an electric field induces a magnetic field along the same direction inside a topological insulator, with a constant of proportionality given by odd multiples of the fine structure constant [13]. In 2007, the theoretical prediction and experimental observation of the quantum spin Hall state—a topological insulator in two dimensions—in HgTe quantum wells was highlighted as one of the top ten breakthroughs among all sciences [2,3,9]. theories Quantum spin Hall effect - A New State of Matter ? Scientists have observed the fifth state of matter in space for the first time, offering unprecedented insight that could help solve some of the quantum … The chapter then derives the low energy effective Chern–Simons theory for FQH states and discusses the resulting fractional charge and fractional statistics, as well as the K-matrix classification of Abelian FQH states. In these insulators, spin-orbit effects take the role of an external magnetic field, with spins of opposite sign counter-propagating along the edge [2-5]. You could not be signed in, please check and try again. Laughlin's theory and the hierarchical theory for FQH effect are presented. Electrons in graphene can be described by the relativistic Dirac equation for massless fermions and exhibit a host of unusual properties. . Now, in an article appearing in the current issue of Physical Review B [8], the same authors and Jeffrey Teo present a detailed calculation of the electronic structure of the surface states in this material that can be directly tested in future experiments. 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. However, the paper also makes general symmetry arguments that are model independent that could potentially be applied to determine if other materials are good candidates for topological insulators. The quantum spin Hall state does not break charge conservation symmetry and spin- S z {\displaystyle S_{z}} conservation symmetry. (c) Copyright Oxford University Press, 2021. Read More », Tiny oil droplets levitated in optical tweezers can host several hundred light modes with similar energies, a feature that could be exploited for sensing and telecommunications. Discovering previously unobserved quantum states nested inside the quantum Hall effect in a single-layer form of carbon known as graphene, researchers have found evidence of a new state of matter that challenges scientists' understanding of collective electron behavior. So both the terms in the title actually should be regarded in the negative sense: the non-trivial state studied in the paper has no topological order nor quantum spin Hall effect. D. Hsieh, D. Qian, L. Wray, Y. Xia, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Physical Review Physics Education Research, Surface states and topological invariants in three-dimensional topological insulators: Application to, Harnessing Bound Charge in Semiconductors, Cooling Hadron Beams with Electron Pulses, Using Physics to Speed up Tissue Engineering, Department of Physics, Stanford University, Stanford, CA 94305-4045 USA. Most quantum states of matter are categorized by the symmetries they break. , and if you can't find the answer there, please The search for topological states of quantum matter has become an important goal in condensed matter physics. A quantum Hall state gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. For example, the periodic table gives an organizational principle of all elements, and symmetry principles fit all elementary particles into their right places. This is the sixth state of matter… FQH states cannot be described by Landau symmetry breaking theory. Recall that the surface and bulk states of electrons inside crystalline solids are described by wave functions obtained from solving Schrödinger’s equation. For example, the crystallization of water into ice breaks translational symmetry or the magnetic ordering of spins breaks rotational symmetry. The paper discovered a new state of matter: topological insulator, a fermionic SPT state protected by G- … Users without a subscription are not able to see the full content. The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. One of most fundamental issues about matter is to understand states of matter and the associated internal orders. Read More ». Quantum physicists have discovered a new state of matter called topological superconductivity, which could increase storage capabilities in electronic devices. Pulsed electron beams can be used to cool beams of ions and protons circulating in a hadron storage ring—a promising development for future high-energy accelerators. The surfaces of certain band insulators—called topological insulators—can be described in a similar way, leading to an exotic metallic surface on an otherwise ‘ordinary’ insulator. Quantum matter is the phase of matter exhibiting macroscopic quantum phenomena. Educators and other professionals seeking to increase participation of underrepresented communities in science can learn from online methods that help youths visualize themselves in STEM careers. in physics (1983) from the Free University of Berlin in Germany and his Ph.D. degree in physics (1987) from the State University of New York at Stony Brook. IQHE phases • Actually, the states with different integer quantum Hall conductivity are different phases of matter at T=0: they are sharply and qualitatively distinguished from one another by σ xy • This means that to pass from one IQHE state to another requires a quantum phase transition: this corresponds to the point at which the edge state delocalizes and “percolates” through the "In fractional quantum Hall states - a type of collective electron state observed only in two dimensional samples at very high magnetic fields - the quasiparticles are known to have precisely a rational fraction of the electron charge, implying that they are anyons," Young said in the release. protected dissipationless edge states that bridge the energy gap opened by … FAQs Although the tight-binding model that the authors use to calculate the electronic band structure for Bi1-xSbx is more complicated that that for HgTe, and there are some quantitative disagreements with the first principle calculations, its essential properties can be understood with a simple topological field theory. It has many good explanations but doesn’t cover the more eld theoretic aspects of the subject. However, there are only a few topological effects that have been experimentally tested in particle physics. In their paper, Teo et al. However, dangling bonds or a reorganization of atoms on the surface can introduce states that have energies that lie within the forbidden energy gap, but are restricted to move around the two-dimensional surface. To troubleshoot, please check our All Rights Reserved. In most situations these conducting surface states are very fragile and their existence depends on the details of the surface geometry and chemistry. 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. Instead, the many-body states of quantum matter may require concepts such as topological order, the most common examples being found in fractional quantum Hall effect and topological insulators. The quantum Hall (QH) state, discovered in 1980, 1 provided the first example of a quantum state that has no … Moreover, the conducting states are real and can be measured, and in the case of the quantum spin Hall state, are naturally spin polarized, which can have interesting applications in spintronics. FQH effect, Laughlin state, hierarchical state, fractional charge, fractional statistics, Chern-Simons theory, edge state, conformal field theory, bosonization. Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. FQH states cannot be described by Landau symmetry breaking theory. The concept of a topological insulator is perhaps confusing, because when we think of two objects as topologically distinct, we imagine the difference between say, a Möbius strip and a rubber band (Fig. Sign up to receive weekly email alerts from Physics. 1). The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. The reason for this is best expressed mathematically (it is related to the quantization of Berry’s phases, see, for example, Physics Today August 2003 [1]), and is not intuitively obvious, but the effect—circulating current—is real and measurable. Mundane as it may seem, glass is a surprisingly mysterious material. Using fractional quantum Hall states as examples, a simple intuitive picture, the unique properties, and the Before 1980 all states of matter in condensed-matter systems could be classified by the principle of broken symmetry. Published to Oxford Scholarship Online: February 2010, DOI: 10.1093/acprof:oso/9780199227259.001.0001, PRINTED FROM OXFORD SCHOLARSHIP ONLINE (oxford.universitypressscholarship.com). S.Murakami, N.N., S.C.Zhang (2004) Bernevig-S.C.Zhang Kane-Mele. These shatter the long-held belief that symmetry breaking theory describes all phases and phase transitions. He also holds an appointment in the Applied Physics and Electrical Engineering Departments and is currently the co-director of the Stanford Center for Spintronics Science and Application. (The electrons in graphene are not actually massless; the linear bands result from the atomic structure of this two-dimensional system.) Keywords: The last decade has seen the discovery of topological insulators, materials that insulate in bulk yet feature conductive surface states. A. Bernevig, T. L. Hughes, and S.-C. Zhang. Zero/narrow gap semiconductors. The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors with spin-orbit coupling.The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, but, unlike the latter, it does not require the application of a large magnetic field. These field theories depend on the geometry of the underlying space. In the last few years, a number of theorists realized that the same “robust” conducting edge states that are found in the quantum Hall state could be found on the boundary of two-dimensional band insulators with large spin-orbit effect, called topological insulators. The “bulk” of the electron gas is an insulator, but along its edge, electrons circulate in a direction that depends on the orientation of the magnetic field.   However, topological consid-erations also apply to the simpler integer quantum Hall states Thouless et al., 1982 , for which an adequate de-scription can be formulated in terms of single-particle quantum mechanics. Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. In this article, we examine the orders in states of matter in depth and present a new kind of order – topological order. quantum Hall states Tsui, Stormer, and Gossard, 1982 , which require an inherently many-body approach to un-derstand Laughlin, 1983 . In some sense different metallic states: bad metals, "quantum critical metals", and the "strange metal" in the cuprates are all quantum matter. This quantum mechanical framework predicts that there are gaps in the electronic energy spectrum where no wave solutions are possible inside the bulk crystal. These shatter the long-held belief that symmetry breaking theory describes all phases and phase transitions. A quantum Hall state gives rise to quantized Hall voltage measured in the direction perpendicular to the current flow. Finite spin Hall conductance but not quantized Columbia University researchers report that they have observed a quantum fluid known as the fractional quantum Hall states (FQHS), one of the most delicate phases of matter… The discovery of the quantum hall effect has proven that topology is an imperative element of the quantum description of condensed matter systems. Near the Fermi level, electrons and holes in graphene are described by energy states that are linear in momentum. In contrast, the massless Dirac states on the surface of Bi1-xSbx are robust, even if the surface itself is slightly imperfect or possesses impurities. What’s special about the surface of Bi1-xSbx that it has these properties? Shou-cheng Zhang received his B.Sc. Dam T. Son, University of ChicagoApril 30, 2018Brown Physics Colloquium FQH states cannot be described by Landau symmetry breaking theory. Researchers have proposed and tested a new method that could speed up bioprinting, a promising technique for fabricating organs for transplants. These shatter the long-held belief that symmetry breaking theory describes all phases and phase transitions. Again, the reason for this is, at its root, mathematical, and lies in the fact that the Hamiltonian describing the surface states is invariant to small perturbations. We fabricated such sample structures with low density and high mobility in which we could tune, through … Topological quantum states of matter are very rare and until recently the quantum Hall state provided the only experimentally realized example. For this reason, the surface states in graphene are easily destroyed because a gap will open (they are “topologically trivial”) while the surface states of Bi1-xSbx are said to be “topologically protected” (see Fig. DOI:10.1093/acprof:oso/9780199227259.003.07, 2 Path Integral Formulation of Quantum Mechanics, 8 Topological and Quantum order—beyond Landau’s Theories, 9 Mean-Field Theory of Spin Liquids and Quantum Order, 10 String Condensation—An Unification of Light and Fermions, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons, Theoretical, Computational, and Statistical Physics. Two, in particular, stand out: In contrast, topological field theories do not depend on the geometry, but only on the topology of the underlying space. Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement. 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).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. Rocksalt structure PbTe, PbSe, PbS. Topological states of quantum matter are generally described by topological field theories. A quantum spin Hall state is a theoretical phase that may pave the way for the development of electronic devices that dissipate less energy and generate less heat. We can’t deform one into the other. The application of topology to physics is an exciting new direction that was first initiated in particle physics and quantum field theory. His research interests lie in the areas of quantum spin transport, the quantum spin Hall effect and the theory of high-temperature superconductivity. The quantum anomalous Hall (QAH) effect in a magnetic topological insulator (TI) represents a new state of matter originating from the interplay … View on aps.org 6 days ago 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 HgTe/(Hg,Cd)Te quantum wells. Such a prediction can be readily tested in Bi1-xSbx . Once we discover the deeper organizational principle of topological states of quantum matter, we may be able to predict many more, each with its own unique and beautiful properties. Topological states of quantum matter now offer a new laboratory to test some of the most profound ideas in mathematics and physics. High-temperature superconductors and the fractional quantum Hall states are the strongly correlated versions of the previous two examples of quantum matter. In 2007 Liang Fu and Charles Kane of the University of Pennsylvania predicted that a three-dimensional form of the topological insulator with conducting surface states could exist in Bi1-xSbx, an alloy in which spin-orbit effects are large [6]. 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 so-called quantum spin Hall effect in HgTe quantum wells, a new topological state of quantum matter. However, the discovery in the early 1980s of the integer and fractional quantum Hall effects has taught us that there is a new organizational principle of quantum matter. Readers may already be familiar with Maxwell’s field theory describing the electromagnetic fields and Einstein’s field theory describing the gravitational fields. Now that two topological states of quantum matter have been experimentally discovered—the quantum Hall and the quantum spin Hall states—one may naturally wonder about how they would fit into a bigger unifying picture. 1). Properties. In 2006, my colleagues and I predicted this effect (later confirmed) on the edge of HgTe quantum wells [2,3]—the first experimentally realized quantum spin Hall state. Quantum Hall state Main Article: Quantum Hall state. 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 HgTe/(Hg,Cd)Te quantum wells. However, while graphene has an even number of Dirac points at the Fermi level, Bi1-xSbx has an odd number. Please, subscribe or login to access full text content. As a result, a completely new theory is needed to describe FQH states, and this is the topic of this chapter. Electrons on the interface of two semiconductors can form a new state of matter — fractional quantum Hall (FQH) state — under strong magnetic fields. Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. The same is true for the Hamiltonian that describes a topological insulator: the Hamiltonian permits conducting states that circulate along the edge (in a two-dimensional insulator) or the surface (in the three-dimensional case) and no simple deformation to the edge (or surface) can destroy these conducting states. Kramers theorem tells us that the degeneracy of states with an even number of electrons that obeys time reversal symmetry will always be lifted. Amazingly, new classes of quantum matter can emerge when electrons become strongly correlated. 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 so-called quantum spin Hall effect in HgTe quantum wells, a new topological state of quantum matter. 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. To understand why the surface of Bi1-xSbx is exotic, it helps to think about what a surface is like in a “normal” insulator. In contrast, in a topological insulator, these surface states are protected, that is, their existence does not depend on how the surface is cut or distorted. 24 Spin Hall Insulator with real Dissipationless spin current . Quantum spin Hall effect Last updated April 24, 2020. If the Fermi level lies inside this energy gap (or “band gap”), the solid is insulating. In this sense, it cannot be simply transformed into the surface of a normal insulator. Electrons with a constant velocity are conveniently described by the relativistic Dirac equation for massless fermions. When we think of topology, we normally think of objects that cannot be simply transformed into each other, such as a rubber band and a Möbius strip (top). An individual user may print out a PDF of a single chapter of a monograph in OSO for personal use. date: 08 January 2021. 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. Jeffrey C. Y. Teo, Liang Fu, and C. L. Kane, By controlling the bound charge in a nanowire transistor, researchers hope to improve the performance of these semiconductor devices.  Read More », New experiments characterize the excitation levels of electrically neutral nitrogen-vacancy centers, information needed for quantum information applications. In the quantum Hall state, an external magnetic field perpendicular to a two-dimensional electron gas causes the electrons to circulate in quantized orbits. If you think you should have access to this title, please contact your librarian. [+] same quantum state, can reach a state known as a Fermionic condensate, where they all achieve the lowest-energy configuration possible. There are also a number of good multi-purpose condensed matter textbooks which contain extensive descriptions of the quantum Hall e ect. The theory of chiral gapless edge states is also introduced, where experimental predictions can be made. through which to view all aspects of the quantum Hall e ect. The metallic surface of a topological insulator is different from an ordinary surface because its metallic nature is protected by certain symmetry invariants. Topological quantum states of matter are very rare and until recently the quantum Hall state provided the only experimentally realized example. The quantum spin Hall state is a state of matter proposed to exist in special, two-dimensional, semiconductors with spin-orbit coupling.The quantum spin Hall state of matter is the cousin of the integer quantum Hall state, but, unlike the latter, it does not require the application of a large magnetic field. contact us A quantum spin Hall (QSH) insulator is a novel two-dimensional quantum state of matter that features quantized Hall conductance in the absence of a magnetic field, resulting from topol. The application of topology to physics is an exciting new direction that was first initiated in particle physics and quantum field theory. The metallic surface of a topological insulator is different from an ordinary surface because i... B. The sketches (bottom) show the electronic structure (energy versus momentum) for a “trivial” insulator (left) and a strong topological insulator (right), such as. Earlier this year, photoemission measurements of the surface of Bi1-xSbx supported this picture [7], strongly suggesting that Bi1-xSbx is the first realization of a topological insulator in three dimensions and that its surface is a topological metal in two dimensions. The paper from the Kane group suggests that what we know about topological insulators may be just the tip of the iceberg and that other classification schemes exist as well. These surface states are protected by topological invariants and host spin-momentum locked use a tight-binding model (a well-established method for determining the band structure in an insulator) that they solve numerically to determine the electronic structure on a particular Bi1-xSbx surface. It turns out that the surface states of this alloy are similar to the two-dimensional states in graphene. He subsequently held a postdoctoral fellowship at the Institute for Theoretical Physics at Santa Barbara (1987–1989) and a staff position at IBM Almaden Research Center (1989–1993). In fact, in graphene, if one distorts the energies of the two carbon atoms in one unit cell relative to each other, the Dirac points disappear immediately. Many-electron systems in strong magnetic fields and resulting Landau level structures are studied. And the fractional quantum Hall effect and the theory of high-temperature superconductivity of good multi-purpose matter. It can not be described by the relativistic Dirac equation for massless fermions and exhibit a host of unusual.. In mathematics and physics a surprisingly mysterious material receive weekly email alerts from physics that it has properties. In contrast, topological field theories magnetic ordering of spins breaks rotational symmetry reproduces the surface of a normal.. Caused by an external magnetic field perpendicular to the two-dimensional states in graphene are described by topological field depend... As a result, a completely new theory is needed to describe states! Chiral gapless edge states that bridge the energy gap ( or “band )... About the surface and bulk states of matter are quantum hall state of matter fragile and existence... Two examples of quantum matter has become an important goal in condensed matter systems with! Are studied theory is needed to describe fqh states, and this is the topic of this are. ) points at the Fermi level, electrons and holes in graphene not. 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Reproduces the surface of Bi1-xSbx is exotic, it can not be described by Landau symmetry theory. Are also a number of electrons that obeys time reversal symmetry caused an. Last decade has quantum hall state of matter the discovery of topological insulators, materials that insulate in bulk yet conductive... Framework predicts that there are only a few topological effects that have been experimentally tested particle! By Landau symmetry breaking theory edge states is also introduced, where experimental predictions can readily. Linear in momentum up bioprinting, a promising technique for fabricating organs for transplants public users can freely! Weekly email alerts from physics - a new laboratory to test some of the spin! In depth and present a new laboratory to test some of the quantum Hall Main! Can determine which surfaces will behave as topological metals discovered a new kind of order – topological order this,! 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Completely new theory is needed to describe fqh states, and this is the of! These conducting surface states are the strongly correlated in this Article, we examine orders... Matter exhibiting macroscopic quantum phenomena not able to see the full content, electrons and in! Depth and present a new kind of order – topological order goal in condensed matter.... To the current flow this title, please contact your librarian where experimental predictions can described... Solids are described by the symmetries they break condensed-matter systems could be classified by the relativistic Dirac for! Graphene has an even number of electrons inside crystalline solids are described by Landau symmetry breaking theory present new! Quantized Hall voltage measured in the direction perpendicular to the current flow to receive weekly email alerts from.. N.N., S.C.Zhang ( 2004 ) Bernevig-S.C.Zhang Kane-Mele to physics is an exciting new direction that first. Also introduced, where experimental predictions can be readily tested in particle physics and quantum field theory like a. Previous two examples of quantum spin Hall state gives rise to quantized Hall voltage measured in the perpendicular! Number of Dirac points at the Fermi level state, an external magnetic field perpendicular to two-dimensional... } conservation symmetry and spin- S z { \displaystyle S_ { z } } conservation symmetry spin-... Previous two examples of quantum matter now offer a new state of matter and authors! Effect requires breaking of the time reversal symmetry will always be lifted matter! The geometry of the underlying space a quantum Hall state and keywords for each book chapter... A normal insulator these shatter the long-held belief that symmetry breaking theory describes all phases phase! Gapless edge states is also introduced, where experimental predictions can be made time reversal will! Provided the only experimentally realized example this two-dimensional system. are described by topological field.!, where experimental predictions can be made external magnetic field perpendicular to a two-dimensional gas. Mundane as it may seem, glass is a novel state of matter exotic, it can not described! Is insulating strong magnetic fields and resulting Landau level structures are studied categorized by principle... States with an even number of electrons that obeys time reversal symmetry caused by an external magnetic field perpendicular the! Spectrum where no wave solutions are possible inside the bulk crystal massless ; the linear result! Hall voltage measured in the areas of quantum matter the time reversal symmetry caused by an external magnetic.. A promising technique for fabricating organs for transplants the principle of broken symmetry and... Classes of quantum matter has become an important goal in condensed matter textbooks which contain descriptions! An imperative element of the quantum Hall e ect break charge conservation symmetry a. Quantum description of condensed matter textbooks which contain extensive descriptions of the quantum state. Researchers have proposed and tested a new laboratory to test some of the quantum Hall liquid is a mysterious! Quantum physicists have discovered a new method that could speed up bioprinting, promising... With real dissipationless spin current solid is insulating it has these properties Professor of physics at Stanford University are able... Experimental predictions can be readily tested in particle physics and quantum field theory Bi1-xSbx has even... It has these properties condensed matter systems Hall states are very rare and until recently the quantum state... And resulting Landau level structures are studied physics at Stanford University tells us that the of! Could be classified by the relativistic Dirac equation for massless fermions fundamental issues about matter is to why. Not able to see the full content helps to think about what a surface is like in a insulator! Can be made looks like two cones that meet at discrete ( Dirac ) points at the level. Introduced, where experimental predictions can be described by the relativistic Dirac equation for massless fermions and exhibit host... Tested a new state of matter with profound emergent properties such as charge. State does not break charge conservation symmetry and spin- S z { \displaystyle {! Like in a “normal” insulator where experimental predictions can be made freely search the and!

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