Particles with fractional statistics interpolating between bosons and fermions have attracted considerable interest from mathematical physicists. / Information about registration may be found here. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta), where p and q are integers with no common factors. We present a microscopic theory of the fractional quantum Hall effect and its hierarchy structure on the basis of a Chern-Simons gauge theory. In 1995, the fractional charge of Laughlin quasiparticles was measured directly in a quantum antidot electrometer at Stony Brook University, New York. See Off-Campus Access to Physical Review for further instructions. There were several major steps in the theory of the FQHE. Google Scholar; 10. The Half-Filled Landau level. Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access. Classically, the Hall conductivity 휎 x y —defined as the ratio of the electrical current to the induced transverse voltage—changes smoothly as the field strength increases. 2 The 1998 Nobel Prize in Physics was awarded to Robert Laughlin, Horst Störmer, and Daniel Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations"[1][2] However, Laughlin's explanation was a phenomenological guess[citation needed] and only applies to fillings The fractional quantum Hall effect results in deep minima in the diagonal resistance, accompanied by exact quantization of the Hall plateaux at fractional filling factors … ©2021 American Physical Society. This effect, termed the fractional quantum Hall effect (FQHE), represents an example of emergent behavior in which electron interactions give rise to collective excitations with properties fundamentally distinct from the fractal IQHE states. ν 4. The fractional quantum Hall effect (FQHE) is a collective behaviour in a two-dimensional system of electrons. The electron's spin degree of freedom may be ignored for present purposes. Here a quantum transport geometry is analyzed, which could provide a link to the fractional statistics … Here q turns out to be an odd number with the exception of two filling factors 5/2 and 7/2. Both of these experiments have been confirmed with certainty. We calculate the statistics of the composite-fermion quasiparticles at ν=1/3 and ν=2/5 by evaluating the Berry phase for a closed loop encircling another composite-fermion quasiparticle. According to this view the only thing to be done is to apply the symmetry breaking theory to all different kinds of phases and phase transitions. Topological Order. Gregory Moore, Nicholas Read, and Xiao-Gang Wen pointed out that non-Abelian statistics can be realized in the fractional quantum Hall effect (FQHE). Composite fermion theory was developed in the process of understanding the fractional quantum Hall efiect and was proven to work successfully for the FQHE and even beyond. Fractional statistics can be extended to nonabelian statistics and examples can be constructed from conformal field theory. https://doi.org/10.1103/PhysRevLett.53.722, Physical Review Physics Education Research, Log in with individual APS Journal Account », Log in with a username/password provided by your institution », Get access through a U.S. public or high school library ». Starting directly from the microscopic Hamiltonian, we derive a field-theory model for the fractional quantum Hall effect. / A more recent experiment,[12] which measures the quasiparticle charge extremely directly, appears beyond reproach. As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. In addition to theoretical foundations, we review the present status of the experiments in the area. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. The Fractional Quantum Hall Effect: PDF Laughlin Wavefunctions, Plasma Analogy, Toy Hamiltonians. All rights reserved. {\displaystyle m} The new type of orders represented by FQH states greatly enrich our Certain fractional quantum Hall phases appear to have the right properties for building a topological quantum computer. The principal series of such fractions are. Not long after the first observation of the fractional quan-tum Hall FQH effect… . By considering an approximate coarse-grained version of the same model, we construct a Landau-Ginzburg theory similar to that of Girvin. In particular magnetic fields, the electron gas condenses into a remarkable liquid state, which is very delicate, requiring high quality material with a low carrier concentration, and extremely low temperatures. Sign up to receive regular email alerts from Physical Review Letters. is an odd integer. Each particular value of the magnetic field corresponds to a filling factor (the ratio of electrons to magnetic flux quanta) These excitations are found to obey fractional statistics, a result closely related to their fractional charge. From this perspective, we can understand the importance of the FQHE discovered by 11. At ・〕ling 1=mthe FQHE state supports quasiparticles with … completely new kind of order—topological order. COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. 3 The Quantum Hall Effects and Fractional Statistics When a thincurrent carrying conductor is subjected toa perpendicular magnetic field B=(0,0,B), there exists a Lorentz force due to the magnetic field acting on the current, which induces an electric field and gives rise to a novel voltage difference, dubbed the “Hall voltage”VH. NA quantum statistics T. H. Hansson Anyon School Berlin, 2013 Fractional quantum statistics T. H. Hansson, Stockholm University Outline: • What is fractional statistics? These excitations are found to obey fractional statistics, a result closely related to their fractional charge. Physical Review Letters™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. A careful consideration of subtle perturbations in the … It is argued that universality classes of fractional quantum Hall systems can be characterized by the quantum numbers and statistics of their excitations. Google Scholar; 9. Particles with fractional statistics interpolating between bosons and fermions have attracted the considerable interest of mathematical physicists. Use of the American Physical Society websites and journals implies that Different FQH states all have the same symmetry where As in the integer quantum Hall effect, the Hall resistance undergoes certain quantum Hall transitions to form a series of plateaus. However, in the case of the FQHE, the origin of the gap is … The statistics of fractional quantum Hall states has been studied in theoretical 6,7 and numerical [8] [9] [10] works. The second part of the book includes a detailed discussion about fractional statistics from the point of view of Chern-Simons theories. The APS Physics logo and Physics logo are trademarks of the American Physical Society. This paper looks at the nature of idealizations and representational structures appealed to in the context of the fractional quantum Hall effect, specifically, with respect to the emergence of anyons and fractional statistics. hibit the fascinating phenomenon of fractional quantum Hall efiect. understanding of quantum phases and quantum phase transitions. We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. Section 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in section 4. To address this, we have been improving access via several different mechanisms. The fractional quantum Hall effect (FQHE) offers a unique laboratory for the experimental study of charge fractionalization. Non-Abelian Quantum Hall States: PDF Higher Landau Levels. Quasi-Holes and Quasi-Particles. The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. the user has read and agrees to our Terms and In particular, in the fractional quantum Hall effect (FQHE) it was suggested early on that the fractionally charged quasiparticle excitations obey fractional statistics [7, 8], that is adiabatic interchange of two identical quasiparti- cles produces a phase not equal to + 1. C. Tsui, Stormer, and Gossard. [14][15], Physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantized plateaus at fractional values of e²/h, What mechanism explains the existence of the, Evidence for fractionally-charged quasiparticles, CS1 maint: multiple names: authors list (, "Physics Nobel Prize Goes to Tsui, Stormer and Laughlin for the Fractional Quantum Hall Effect", "In situ biaxial rotation at low-temperatures in high magnetic fields", "Two-Dimensional Magnetotransport in the Extreme Quantum Limit", "Nobel Lecture: The fractional quantum Hall effect", https://en.wikipedia.org/w/index.php?title=Fractional_quantum_Hall_effect&oldid=1002591991, Articles with unsourced statements from June 2015, Creative Commons Attribution-ShareAlike License, This page was last edited on 25 January 2021, at 04:21. Abstract The statistics of quasiparticles entering the quantum Hall effect are deduced from the adiabatic theorem. Topics covered here includes Chern-Simons field theories, charged vortices, anyon superconductivity and the fractional quantum Hall effect. Conditions and any applicable

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