COLLECTIVE PHENOMENA IN THE QUANTUM HALL EFFECT

The main phenomenological features of Integer Quantum Hall Effect (IQHE) and Fractional Quantum Hall Effect (FQHE) are reviewed. A theory is proposed based on a new basis for the single particle states, given by a representation of the Magnetic Translation Group (MTG).

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THE CONNECTION BETWEEN INTEGER QUANTUM HALL EFFECT AND FRACTIONAL QUANTUM HALL EFFECT

Modern Physics Letters B ◽

10.1142/s0217984907012530 ◽

2007 ◽

Vol 21 (02n03) ◽

pp. 109-113

Author(s):

JE HUAN KOO ◽

GUANGSUP CHO

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Fractional Quantum Hall Effect ◽

Matter Wave ◽

Hall Resistance ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Integer Quantum Hall Effect ◽

Integer Quantum

We investigate the integer quantum Hall effect (IQHE) and the fractional quantum Hall effect (FQHE). We derive the quantized Hall resistance of IQHE in the presence of the high magnetic field using the scheme of standing waves by de Broglie matter wave of electron gas confined within a two-dimensional square-type quantum well. Without any modification of electrons and holes, it is shown that FQHE is only a decoupling mode of the Hall resistance by two-band-type of electrons and holes, which are governed by IQHE respectively.

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Theoretical, Unified Derivation of Both the Integer Quantum Hall Effect and Fractional Quantum Hall Effect

10.20944/preprints202112.0072.v1 ◽

2021 ◽

Author(s):

Shinichi Ishiguri

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Fractional Quantum Hall Effect ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Integer Quantum Hall Effect ◽

Charge Quantization ◽

Integer Quantum ◽

Dimensional Wave

In this paper, using the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the balance between the Lorentz force and electrical force, we succeed in deriving the fractional quantum Hall effect and the integer quantum Hall effect; we find that the latter exists as a special case of the former. Moreover, using the derived expression describing the fractional quantum Hall effect, a relationship between the plateau in the resistivity of the sample and the applied magnetic field is obtained. The findings of this model agree well with experimental measurements. Because the two integers that describe the stationary 2-dimensional wave and the charge quantization along with the force balance have concrete physical meanings in this work, we could provide a clear picture of the origin of both the integer quantum Hall effect and the fractional quantum Hall effect.

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A COULOMB GAS DESCRIPTION OF THE COLLECTIVE STATES FOR THE FRACTIONAL QUANTUM HALL EFFECT

Modern Physics Letters A ◽

10.1142/s0217732391001925 ◽

1991 ◽

Vol 06 (19) ◽

pp. 1779-1786 ◽

Cited By ~ 15

Author(s):

G. CRISTOFANO ◽

G. MAIELLA ◽

R. MUSTO ◽

F. NICODEMI

Keyword(s):

Hall Effect ◽

Quantum Hall Effect ◽

Quantum Hall ◽

Coulomb Gas ◽

Fractional Quantum Hall Effect ◽

Irreducible Representations ◽

Vertex Operators ◽

Fractional Quantum ◽

Fractional Quantum Hall ◽

Magnetic Translation

Many anyons wavefunctions relevant for the fractional Quantum Hall Effect at filling ν = 1/m are obtained by using Coulomb gas conformal Vertex operators. They provide irreducible representations of a subgroup of the magnetic translation group on the torus and their degeneracy is related to the allowed set of anyonic charges.

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