Energy gap in fractional quantum Hall effect

ISRN Condensed Matter Physics

2014

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The fractional quantum Hall (FQH) states with higher Landau levels have new characters different from those with 0<ν<2. The FQH states at 2<ν<3 are examined by developing the Tao-Thouless theory. We can find a unique configuration of electrons with the minimum Coulomb energy in the Landau orbitals. Therein the electron (or hole) pairs placed in the first and second nearest Landau orbitals can transfer to all the empty (or filled) orbitals at ν0=8/3, 14/5, 7/3, 11/5, and 5/2 via the Coulomb interaction. More distant electron (or hole) pairs with the same centre position have the same total momentum. Therefore, these pairs can also transfer to all the empty (or filled) orbitals. The sum of the pair energies from these quantum transitions yields a minimum at ν=ν0. The spectrum of the pair energy takes the lowest value at ν0 and a higher value with a gap in the neighbourhood of ν0 because many transitions are forbidden at a deviated filling factor from ν0. From the theoretical result, the FQH states with ν=ν0 are stable and the plateaus appear at the specific filling factors ν0.

Section: Introductionmentioning

confidence: 99%

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

ISRN Condensed Matter Physics

2014

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“…The conservation law produces energy gaps for the specific filling factors. For the other filling factors, we have found the gapless structure and peak structure [17][18][19][20][21][22][23]. The theory can well explain the behaviors of the FQHE at ] < 2 without any quasi particles.…”

Section: Introductionmentioning

confidence: 83%

“…In this paper, we calculate the spinpolarization versus magnetic field at ] < 2 by developing the previous method in the references [17][18][19][20][21][22][23]. Kukushkin et al have measured the electron spinpolarization versus magnetic field [50].…”

Section: Introductionmentioning

confidence: 99%

Spin Polarization Curve of Fractional Quantum Hall States with Filling Factor Smaller than 2

ISRN Condensed Matter Physics

2013

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Kukushkin et al. have measured the electron spin polarization versus magnetic field in the fractional quantum Hall states. The polarization curves show wide plateaus and small shoulders. The 2D electron system is described by the total Hamiltonian ( + ). Therein, is the sum of the Landau energies and classical Coulomb energies. is the residual interaction yielding Coulomb transitions. It is proven for any filling factor that the most uniform electron configuration in the Landau states is only one. The configuration has the minimum energy of . When the magnetic field is weak, some electrons have up-spins and the others downspins. Then, there are many spin arrangements. These spin arrangements give the degenerate ground states of . We consider the partial Hamiltonian only between the ground states. The partial Hamiltonian yields the Peierls instability and is diagonalized exactly. The sum of the classical Coulomb and spin exchange energies has minimum for an interval modulation between Landau orbitals. Using the solution with the minimum energy, the spin polarization is calculated which reproduces the wide plateaus and small shoulders. The theoretical result is in good agreement with the experimental data.

“…This precise confinement of Hall resistance means the existence of an energy gap in the energy spectrum for these filling factors. The energy gap is discussed by many theorists; for examples, in references [5,11,13]. The energy per electron ! "…”

Section: Introductionmentioning

confidence: 99%

“…# ( ) versus filling factor ! " is the sum of Landau energy, classical Coulomb energy, and quantum transition energy [11]. The Landau energy is the eigenenergy of a single electron, neglecting Coulomb interaction; it depends upon magnetic field…”

Section: Introductionmentioning

confidence: 99%

Movement of diagonal resistivity in fractional quantum hall effect via periodic modulation of magnetic field strength

2008

J. Phys.: Conf. Ser.

Energy spectrum of fractional quantum Hall (FQH) states is composed of single electron energy (Landau energy) neglecting the Coulomb interactions between electrons, classical Coulomb energy and the quantum energy via quantum transitions. Herein, the sum of the Landau energy and the classical Coulomb energy depends upon the value of the filling factor continuously. However, the quantum transition energy discontinuously depends upon the value of the filling factor. This discontinuity yields energy gaps in many stable FQH states. The energy gaps for specific filling factors produce the precise confinement of Hall resistance.A new experiment is considered as follows; the magnetic strength is fixed to the value to confine the Hall resistance at the filling factor of 2/3 as an example. Moreover the magnetic modulation with frequency f is applied to the system. The frequency dependence of the diagonal resistance is measured.Then, it is shown in this paper that the diagonal resistance varies drastically at some frequency value f 0 .We clarify the following relation between this value f 0 and the magnetic strength width dB of Hall plateaus as f 0 = e dB / (4 Pi m), where -e is the charge of electron, Pi =3.141592, and m is the mass of electron.for the Hall device used in reference [1]. Drastic increment of diagonal resistanceWe consider a new experiment as:(1) The magnetic field strength is fixed to maintain the FQH state with ! " = 2 3.(2) A periodic magnetic modulation is added to the system. The frequency value is ! f . (3) The diagonal resistance ! R xx is measured. Then the value of ! R xx depends upon the oscillation frequency ! f . The behaviour of ! R xx versus ! f is predicted as shown in figure 3.