Plateaus in the Hall Resistance Curve at Filling Factors <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mn>2</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>ν</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>3</mml:mn></mml:math>

Sasaki, Shosuke

doi:10.1155/2014/468130

Cited by 2 publications

(2 citation statements)

References 38 publications

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“…Thereby, the Hall confinement appears at the specific filling factors. Thus the present theory can explain the FQHE well without any quasi-particle [21]- [26].…”

Section: Introductionsupporting

confidence: 50%

Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2

Sasaki¹

2015

JMP

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The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Hall effect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interaction yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polarization curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge distribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin exchange interaction should be treated exactly. We have succeeded in diagonalizing the spin exchange interaction for the first and second nearest electron pairs. The theoretical results reproduce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamiltonian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.

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“…Thereby, the Hall confinement appears at the specific filling factors. Thus the present theory can explain the FQHE well without any quasi-particle [21]- [26].…”

Section: Introductionsupporting

confidence: 50%

Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2

Sasaki¹

2015

JMP

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“…Any non-nearest pair interleaves one or more Landau orbitals inside the pair. We have examined this effect in details in the article [12]. The energies of the non-nearest pairs are smaller than that of the nearest pairs for 2 ν < .…”

Section: Spectrum Of the Total Energy Versus Filling Factormentioning

confidence: 98%

Relation between FQHE Plateau Width and Valley Energy

Sasaki¹

2015

JMP

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We have investigated the Fractional Quantum Hall Effect (FQHE) on the fundamental Hamiltonian with the Coulomb interactions between normal electrons without any quasi particle. The electron pairs placed in the Landau orbitals can transfer to many empty orbitals. The number of the quantum transitions decreases discontinuously when the filling factor ν deviates from the specific fractional number of ν0. The discontinuous decreasing produces the energy valley at the specific filling factors ν0 = 2/3, 4/5, 3/5, 4/7, 3/7, 2/5, 1/3 and so on. The diagonal elements of the total Hamiltonian and the number of the quantum transitions give the total energy of the FQH states. The energy per electron has the discontinuous spectrum depending on the filling factor ν. We obtain the function form of the energy per electron in the quantum Hall system. Then the theoretical Hall resistance curve is calculated near several filling factors. Therein the quantum Hall plateaus are derived from the energy valleys. The depths of the energy valleys are compared with the widths of the quantum Hall plateaus appearing in the experimental data of the Hall resistance. Our theoretical results are in good agreement with the experimental results.

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Plateaus in the Hall Resistance Curve at Filling Factors 2<ν<3

Cited by 2 publications

References 38 publications

Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2

Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2

Relation between FQHE Plateau Width and Valley Energy

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Plateaus in the Hall Resistance Curve at Filling Factors 2<ν<3

Cited by 2 publications

References 38 publications

Spin Polarization of Fractional Quantum Hall States with &lt;i&gt;ν&lt;/i&gt; &lt; 2

Spin Polarization of Fractional Quantum Hall States with &lt;i&gt;ν&lt;/i&gt; &lt; 2

Relation between FQHE Plateau Width and Valley Energy

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Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2

Spin Polarization of Fractional Quantum Hall States with <i>ν</i> < 2