Fractional Quantization of the Hall Effect

Störmer, H. L.; Chang, A. M.; Tsui, D. C.; Hwang, J.C.M.; Gossard, A. C.; Wiegmann, W.

doi:10.1103/physrevlett.50.1953

Cited by 318 publications

(96 citation statements)

References 17 publications

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“…Later with increasing quality of the 2DES and lower temperature, for n certain additional fractional numbers f have been discovered [10] (Nobel prize in 1998), which seem to follow f = p/q with p = {1, 2, 3, . .…”

Section: Some Basics Of the Quantum Hall Effectmentioning

confidence: 99%

Metrology and microscopic picture of the integer quantum Hall effect

Weis

Klitzing

2011

Phil. Trans. R. Soc. A.

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Since 1990, the integer quantum Hall effect has provided the electrical resistance standard, and there has been a firm belief that the measured quantum Hall resistances are described only by fundamental physical constants-the elementary charge e and the Planck constant h. The metrological application seems not to rely on detailed knowledge of the microscopic picture of the quantum Hall effect; however, technical guidelines are recommended to confirm the quality of the sample to confirm the exactness of the measured resistance value. In this paper, we give our present understanding of the microscopic picture, derived from systematic scanning force microscopy investigations on GaAs/(AlGa)As quantum Hall samples, and relate these to the technical guidelines.

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Section: Some Basics Of the Quantum Hall Effectmentioning

confidence: 99%

Metrology and microscopic picture of the integer quantum Hall effect

Weis

Klitzing

2011

Phil. Trans. R. Soc. A.

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“…Therefore, we expect that the minima of the diagonal-resistivity appear at these sites. This expectation can be proved by the experimental data [1][2][3]5] on the integral and fractional QHEs as follows. In order to compare the theoretical results with the experimental data, we rewrite the truncation condition as…”

Section: Quantum Hall Plateaus and Their Widthsmentioning

confidence: 86%

“…where ν ( ) | | is defined as the theoretical filling factor by comparison with the experimental one ν in references [1][2][3]5], parameter is related to the sample properties and electronic densities, and can be determined by a single set of experimental data. For example, if we take = 0 067 ≈ 13, then Eq.…”

Section: Quantum Hall Plateaus and Their Widthsmentioning

confidence: 99%

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A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

Hai

Xiao

2011

Open Physics

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Ê Ú ¾ ÂÙÒ ¾¼½½ ÔØ ¾ ÂÙÐÝ ¾¼½½ ×ØÖ ØIt is previously found that the two-dimensional (2D) electron-pair in a homogeneous magnetic field has a set of exact solutions for a denumerably infinite set of magnetic fields. Here we demonstrate that as a function of magnetic field a band-like structure of energy associated with the exact pair states exists. A direct and simple connection between the pair states and the quantum Hall effect is revealed by the band-like structure of the hydrogen "pseudo-atom". From such a connection one can predict the sites and widths of the integral and fractional quantum Hall plateaus for an electron gas in a GaAs-Al Ga 1− As heterojunction. The results are in good agreement with the existing experimental data.

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“…[1,6,7]. For the symmetry class A of the quantum Hall effect in 2D, i.e., no symmetries except a local U(1) charge conservation, there is a variety of topological phases apart from the integer quantum Hall (IQH) phases [8][9][10], namely the family of fractional quantum Hall states [11][12][13] that exist only in the presence of interactions and hence cannot be adiabatically deformed into non-interacting band structures. These phases can be classified in the framework of topological order which was introduced by Wen back in 1990 [14].…”

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Charge conservation protected topological phases

Budich

2013

Phys. Rev. B

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We discuss the relation between particle number conservation and topological phases. In four spatial dimensions, we find that systems belonging to different topological phases in the presence of a U(1) charge conservation can be connected adiabatically, i.e., without closing the gap, upon intermediately breaking this local symmetry by a superconducting term. The time reversal preserving topological insulator states in 2D and 3D which can be obtained from the 4D parent state by dimensional reduction inherit this protection by charge conservation. Hence, all topological insulators can be adiabatically connected to a trivial insulating state without breaking time reversal symmetry, provided an intermediate superconducting term is allowed during the adiabatic deformation. Conversely, in one spatial dimension, non-symmetry-protected topological phases occur only in systems that break U(1) charge conservation. These results can intuitively be understood by considering a natural embedding of the classifying spaces of charge conserving Hamiltonians into the corresponding Bogoliubov de Gennes classes.Introduction -In recent years, topological states of matter (TSM) that can be understood at the level of quadratic model Hamiltonians have become a major focus of condensed matter physics [1][2][3][4]. An exhaustive classification of all possible TSM in the ten AltlandZirnbauer symmetry classes [5] of insulators and mean field superconductors has been achieved by different means in Refs. [1,6,7]. For the symmetry class A of the quantum Hall effect in 2D, i.e., no symmetries except a local U(1) charge conservation, there is a variety of topological phases apart from the integer quantum Hall (IQH) phases [8][9][10], namely the family of fractional quantum Hall states [11][12][13] that exist only in the presence of interactions and hence cannot be adiabatically deformed into non-interacting band structures. These phases can be classified in the framework of topological order which was introduced by Wen back in 1990 [14]. In a more recent paper by Chen, Gu, and Wen [15], it has been shown that different gapped phases which do not have local order parameters associated with spontaneous symmetry breaking must have different topological orders. Furthermore, Ref.[15] identifies different topological orders with different patterns of long range entanglement (LRE).

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Fractional Quantization of the Hall Effect

Cited by 318 publications

References 17 publications

Metrology and microscopic picture of the integer quantum Hall effect

Metrology and microscopic picture of the integer quantum Hall effect

A direct connection between quantum Hall plateaus and exact pair states in a 2D electron gas

Charge conservation protected topological phases

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