Quantum theory of the Hall effect

Ghaboussi, F.

doi:10.1007/bf02435792

Cited by 3 publications

(4 citation statements)

References 14 publications

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“…Balachandran, and others [16,17,18]. Recently, Ghabhoussi claimed the fundamental validity of the Chern-Simons Lagrangian for the integral quantum Hall effect [18].…”

Section: Contentsmentioning

confidence: 98%

“…yielding the correct statistics phase factor even in the ABAC inspired picture. 5 Thus, if the picture is true, a prerequesite for building the macroscopic Bose-condensed QHE state, is the validity of the Chern-Simons dynamics, a fact emphasized by Fröhlich, Balachandran, and others [16,17,18]. Recently, Ghabhoussi claimed the fundamental validity of the Chern-Simons Lagrangian for the integral quantum Hall effect [18].…”

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confidence: 96%

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Robustness of the Quantum Hall Effect, Sample Size Versus Sample Topology, and Quality Control Management of III–V Molecular Beam Epitaxy

Tscheuschner

Hoch

Leschinsky

et al. 1998

Int. J. Mod. Phys. B

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We measure the IQHE on macroscopic (1.5 cm × 1.5 cm) "quick and dirty" prepared III-V heterostucture samples with van der Pauw and modified Corbino geometries at 1.3 K. We compare our results with (i) data taken on smaller specimens, among them samples with a standard Hall bar geometry, (ii) results of our numerical analysis taking inhomogenities of the 2DEG into account. Our main finding is a confirmation of the expected robustness of the IQHE which favours the development of wide plateaux for small filling factors and very large samples sizes (here with areas 10 000 times larger than in standard arrangements).

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“…Balachandran, and others [16,17,18]. Recently, Ghabhoussi claimed the fundamental validity of the Chern-Simons Lagrangian for the integral quantum Hall effect [18].…”

Section: Contentsmentioning

confidence: 98%

mentioning

confidence: 96%

Robustness of the Quantum Hall Effect, Sample Size Versus Sample Topology, and Quality Control Management of III–V Molecular Beam Epitaxy

Tscheuschner

Hoch

Leschinsky

et al. 1998

Int. J. Mod. Phys. B

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“…I t i s e a s i l y s h o w n t h a t a f a c t o r s y s t e m corresponds to the representations given by (5). It can be proven [12,13] that this factor system corresponds to the Landau gauge, used in many papers [8,14]. Discussion on a form of vector potential and gauge invariance lies beyond the scope of this work and it is presented elsewhere [12].…”

Section: Irreducible Projective Representationsmentioning

confidence: 92%

“…A general formula (14) for multiplicities of irreducible projective representations in a product of two others is given. It is important that the introduced irreducible representations (10) can be written as a product of a one-dimensional irreducible representation (k) of the translation group Ty i n E q .…”

Section: Final Remarks and Conclusionmentioning

confidence: 99%

Product of Projective Representations in Description of Multi-Electron States in An External Magnetic Field

Florek

1999

Acta Phys. Pol. A

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In this paper all inequivalent irreducible projective representations of the two-dimensional translation group for a given factor system are determined. A normalized, i.e. corresponding to the Landau gauge, factor system is considered. Obtained representations directly lead to concept of magnetic cells and to periodicity with respect to the charge of a moving particle. It is also shown that the quantization condition is imposed on the product qH of the charge q and the magnitude of magnetic field H. The Kronecker product of such representations is considered and it is proven that the multiplication of representations corresponds to the addition of charges of particles moving in a given external magnetic field. In general, coupling of d representations corresponds to d-particle states. Presented results can be applied in any problem related to two-dimensional electron gas in a magnetic field, for example in the fractional quantum Hall effect or high temperature superconductivity.

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Constraints on Noncommutative Hall Effect Revisited

Godinho

2008

Int. J. Mod. Phys. A

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We consider a semiclassical formulation of the quantum Hall effect by means of an Chern–Simons gauge theory constructed for a Schrödinger field. We build up constraints managing the Faddeev–Jackiw algorithm and show a direct relation of the constraints with Hall conductivity. In the second step, we consider the noncommutative extension to the action computing the new and more general constraints and, as a right consequence, an interesting correction for the conductivity expression is found. Finally, we speculate possible interpretations of this new result and its consequences.

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Quantum theory of the Hall effect

Cited by 3 publications

References 14 publications

Robustness of the Quantum Hall Effect, Sample Size Versus Sample Topology, and Quality Control Management of III–V Molecular Beam Epitaxy

Robustness of the Quantum Hall Effect, Sample Size Versus Sample Topology, and Quality Control Management of III–V Molecular Beam Epitaxy

Product of Projective Representations in Description of Multi-Electron States in An External Magnetic Field

Constraints on Noncommutative Hall Effect Revisited

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