Introduction to the fractional quantum hall e ect steven m. Quantum hall effect classic 3d bz, ex in a conductor. Tunneling experiments in the fractional quantum hall e ect regime. T he incom pressible states m entioned above have unique propertie s unlike any previously know n.
Evidence for a fractional fractal quantum hall effect in. It implies, that many electrons, acting in concert, can create new par ticles. Pdf the classical hall effect, the integer quantum hall effect and the fractional quantum hall effect. In addition to being an interesting system in its own right, the fractional quantum hall effect is also interesting from the. We show the emergence of 1d states with densitywave and clustering order, related to topology, at odd denominator fillings that appear also in the fractional quantum hall effect fqhe, which is a 2d. However, electrons commonly favor an incompressible liquid state, the fractional quantum hall fqh liquid, instead of the. The fractional quantum hall effect looks to the eye like the integral quantum hall effect, except that the hall conductance, in the case of the step, is e2 h. Magnet lab press release quantum hall effect observed at room.
The thermal kh and electrical gh hall conductances are thus simply related by the wiedemannfranz law for free electrons. Fractional quantum hall effect, rotating bosons and abelian. Related content matrix effective theories of the fractional quantum hall effect andrea cappelli and ivan d rodriguezlectures on holographic. 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 tsui et al. The quasiparticles relevant to the physics of the fqhe were predicted theoretically and con. While the integer qh effect can be understood in terms of the landau quantization of noninteracting electrons, the fractional qh state is a strongly correlated quantum liquid, where electronelectron interactions play.
Fractional quantum hall effect conformal field theory and. Pdf orbifold fractional quantum hall effect matilde. Quantum hall effect, in 1982, the fractional quantum hall effect was discovered by stormer, tsui, and. The quantum hall effect department of applied mathematics and. Abstract we study the quantum selforganization of interacting particles in onedimensional 1d manybody systems, modeled via hubbard chains with shortrange interactions between the particles. On the effective hydrodynamics of the fractional quantum hall effect to cite this article. Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum hall effect. E y j x hall resistivity, transverse r h e y j xb z. The above sequences account for most, but not all, observed fractions. More specifically, this is done by looking at the anomaly in the current conservation equation of a wznw theory describing fields living at the. Dirac composite fermions the fractional quantum hall e ect occurs when landau levels are fractionally lled. Chapter 1 is the introductory chapter to this thesis.
Despite enormous theoretical and experimental effort during the past decade, the nature of transport in the fractional quantum hall effect fqhe. Introduction to the fractional quantum hall effect seminaire poincare. The main assertion is that new candidate incompressible states can be constructed by taking products of some known incompressible states, and all incompressible states can thus be generated starting from the states at integer filling factors. Motivated by the parton theory of the fqhe, we consider the possibility of a new kind of emergent superconductivity in the fqhe, which involves.
This quantum hall effect is referred to as the quantum anomalous hall qah effect. Laughlin wave function the fractional qhe is evidently prima facie impossible to obtain within an independentelectron picture, since it would appear to require that the extended states be only partially. Pdf fractional quantum hall effect from anomalies in wznw. The quantum hall effect is referred to as the integer or fractional quantum hall effect depending on whether. Laughlin, fractional quantization, december 8th, 1998. Both discoveries were awarded with nobel prizes, with regard to iqhe for k. The fractional quantum hall effect explains the fractional quantization of transverse conductance in the presence of a magnetic field. Fractional quantum hall effect an overview sciencedirect. A number of these are understood as fractional quantum hall effect of composite fermions. 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. Integer and fractional quantum hall effects system zeus umcs.
This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum hall effect. The fractional quantum hall effect fqhe is a collective behaviour in a twodimensional system of electrons. Berry phase, aharonovbohm effect, nonabelian berry holonomy. 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. The rich phenomenology of the quantum hall qh effect provides a fertile setting for the study of correlated electrons 1. Recent research has uncovered a fascinating quantum liquid made up solely of. Again, the hall conductivity exhibits a plateau, but in this case quantized to fractions of e 2 h. However, in the case of the fqhe, the origin of the gap is different from that in the case of the iqhe. The dirac composite fermions in fractional quantum hall effect dam thanh son university of chicago nambu memorial symposium march 12, 2016. While very elegant and appealing, the picture of refs.
The fractional quantum hall effect department of applied. Stormer department of physics and department of applied physics, columbia university, new york, new york 10023 and bell labs, lucent technologies, murray hill, new jersey 07974 s0034686199007047 introduction the fractional quantum hall effect is a very counter. This is similar to the hall conductivity of a massless dirac fermion with timereversal symmetry broken by a mass term m. Charles kittel, introduction to solid state physics. We can explain the mutual statistic of laughlin quasiparticles d. Our detection of phase slips in quantum interference experiments demonstrates a powerful, new way of detecting braiding of anyons. Using this tool, numerous tests have been performed to check the validity of e ective theories commonly used to calculate observable quantities in the fractional quantum hall e ect fqhe. The fractional quantum hall effect is a very counterintuitive physical pheno menon. Quantized thermal transport in the fractional quantum hall effect. Electronhole asymmetric integer and fractional quantum hall.
Girvin yale university sloane physics laboratory new haven, ct 06520 usa 1 introduction the quantum hall e ect qhe is one of the most remarkable condensedmatter phenomena discovered in the second half of the 20th century. Quantum hall effect emergence in the fractional quantum hall effect abstract student luis ramirez the experimental discovery of the fractional quantum hall effect fqhe in 1980 was followed by attempts to explain it in terms of the emergence of a novel type of quantum liquid. Tsui for their discovery of a new form of quantum fluid with fractionally charged excitations. Let us consider an annulus whose electrons are in a fractional quantum hall state. At high magnetic fields, the kinetic energy of electrons is suppressed, which favors wigner crystallization of electrons to a lattice. A similar quantization of the thermal conductance occurs for a quantum point contact. Fractional charge and fractional statistics in the quantum. Pdf theory of the integer and fractional quantum hall effects. Fractional quantum hall effect and featureless mott insulators. The fractional quantum hall e ect provides a unique example of a quantum system with fractional quantum numbers.
Each such liquid is characterized by a fractional quantum number that is directly observable in a simple electrical measurement. Fractional quantum hall effect fqhe tsui, stormer, gossard, 1982 e2 h r xy. Coulomb blockade in the fractional quantum hall effect regime. This project seeks to articulate a notion of emergence that is. Topological phases of matter and fractional quantum hall effect. Competition between liquid and solid states in twodimensional electron system is an intriguing problem in condensed matter physics. Fractional quantum hall effect in an array of quantum wires. Similar to the iqhe, this is the result of gaps in the density of states, unlike the iqhe, however, it is not possible to explain the presence of such. The fractional quantum hall effect is also understood as an integer quantum hall effect, although not of electrons but of chargeflux composites known as composite fermions. An approach to understand fractional quantum hall effect fqhe using anomalies is studied in this paper. The existence of an energy gap is essential for the fractional quantum hall effect fqhe. In 1988, it was proposed that there was quantum hall effect without landau levels.
Introduction to the fractional quantum hall effect. Weve come to a pretty good understanding of the integer quantum hall effect and the reasons behind its robustness. The nobel prize in physics 1998 was awarded jointly to robert b. M uch is understood about the fractiona l quantum h all effect. Theory of the integer and fractional quantum hall effects. Grayson eecs, nuthe workshop on semiconductors, electronic materials, thin films and photonic materialstel aviv universityfebruary 22. Their use has definitely had an impact on our understanding of quantum effects in solid state thin films e. In this paper, we report on the study of abelian and nonabelian statistics through fabryperot interferometry of fractional quantum hall fqh systems. A theoretical framework is presented which provides a unified description of the integer and the fractional quantum hall effects. The fractional quantum hall fqh effect is reported in a high mobility cdte quantum well at millikelvin temperatures.
Later also plateaus at intermediate values of hall voltages were measured 2. The topological pwave pairing of composite fermions, believed to be responsible for the 52 fractional quantum hall effect fqhe, has generated much exciting physics. Plan fractional quantum hall effect halperinleeread hlr theory problem of particlehole symmetry dirac composite fermion theory consequences, relationship to. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. Other fractions have been observed, which arise from a weak residual interaction between composite fermions, and are thus more delicate. Fractional quantum hall e ect conformal field theory and matrix product states benoit estienne lpthe, paris entanglement in strongly correlated systems benasque benoit estienne lpthe matrix product state for fqhs 2016, feb 18 1 53. Fractionalquantumhalleffect fqhe in 1d hubbard models. Homotopy approach to fractional quantum hall effect. The many electrons inside an ultrathin layer construct a quasitwodimensional quasi2d. The fractional quantum hall effect particle theory group. The dirac composite fermions in fractional quantum hall effect. On the effective hydrodynamics of the fractional quantum hall. Braiding of abelian and nonabelian anyons in the fractional.
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