Quantized Hall conductance was discovered in 1980, related to the electron charge. As of 2011 he is developing a new geometric description of the fractional quantum Hall effect that introduces the "shape" of the "composite boson", described by a "unimodular" (determinant 1) spatial metric-tensor field as the fundamental collective degree of freedom of Fractional quantum Hall effect … Lett., 53, 722 (1984), "Fractional Statistics and the Quantum Hall Effect" The resulting many-particle states (Laughlin, 1983) are of an inherently quantum-mechanical nature. The experimental discovery of the fractional quantum Hall effect (FQHE) at the end of 1981 by Tsui, Stormer and Gossard was absolutely unexpected since, at this time, no theoretical work existed that could predict new struc­ tures in the magnetotransport coefficients under conditions representing the extreme quantum limit. The Integer Quantum Hall Effect: PDF Conductivity and Edge Modes. (1982), with f=1/3 and 2/3 the most prominent examples. Here, we construct a different type of fractional quantum Hall system, which has the special property that it lives in fractal dimensions. The classical Hall effect, the integer quantum Hall effect and the fractional quantum Hall effect. The fractional quantum Hall effect is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e 2 / h {\displaystyle e^{2}/h} . Characterization of topological order. Disorder and Gauge Invariance. Rev. Its driving force is the reduc-tion of Coulomb interaction between the like-charged electrons. The Kubo formula. The fractional quantum Hall effect is the result of the highly correlated motion of many electrons in 2D ex-posed to a magnetic field. Nowadays this effect is denoted as integer quantum Hall effect (IQHE) since, for 2DESs of higher quality and at lower temperature, plateau values in the Hall resistance have been found with by | R H |=h/(fe 2), where f is a fractional number, Tsui et al. Xiao-Gang Wen, Quantum Field Theory of Many Body Systems – From the Origin of Sound to an Origin of Light and Electrons, Oxford Univ. The fractional quantum Hall effect is a paradigm of topological order and has been studied thoroughly in two dimensions. Abstract: Multicomponent quantum Hall effect, under the interplay between intercomponent and intracomponent correlations, leads us to new emergent topological orders. Laughlin proposed a fluid of fractional charges in 1983, to explain the fractional quantum Hall effect seen in 1982, for which he shared the 1998 Physics Nobel Prize. A theoretical framework is presented which provides a unified description of the integer and the fractional quantum Hall effects. The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of /.It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles, and excitations have a fractional elementary charge and possibly also fractional statistics. In 1997, experiments directly observed an electric current of … D. Arovas and J. R. Schrieffer and F. Wilczek, Phys. 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. Landau levels, Landau gauge and symmetric gauge. Press, Oxford, 2004. Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy; 2. Has been studied thoroughly in two dimensions the integer and the fractional quantum Hall effect under... 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