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

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Shosuke Sasaki
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Total Momentum ◽  
Landau Levels ◽  
Coulomb Energy ◽  
Hall Resistance ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Transitions ◽  
Pair Energy

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.

scholarly journals PHONON EXCITATIONS OF COMPOSITE FERMION LANDAU LEVELS

2004 ◽  
Vol 18 (27n29) ◽  
pp. 3857-3864 ◽  
Author(s):  
F. SCHULZE-WISCHELER ◽  
F. HOHLS ◽  
U. ZEITLER ◽  
D. REUTER ◽  
A. D. WIECK ◽  
...  
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Landau Levels ◽  
Composite Fermion ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall Regime ◽  
Hall Regime ◽  
The Magnetic Field ◽  
Linear Field

Energy gaps in the fractional quantum Hall regime are measured with phonon spectroscopy for various electron densities and filling factors ν=1/3, 2/5, 4/7, 3/5, 2/3, 4/3, and 5/3. At a given filling factor nearly all gaps measured show a square-root dependence on the magnetic field. The measured gaps can be described well with composite fermion theory: They are transitions between composite fermion Landau levels that are not affected by disorder on phonon wavelength. All transitions can be described by one single fit parameter related to the composite fermion effective mass. In contrast, the gaps at filling factor ν=2/3 in the high fields regime show a linear field dependence. This hints onto an only partially polarized ground state of 2/3.

scholarly journals Local incompressibility of fractional quantum Hall states at a filling factor of 3/2

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
L. V. Kulik ◽  
V. A. Kuznetsov ◽  
A. S. Zhuravlev ◽  
V. Umansky ◽  
I. V. Kukushkin
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

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

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.

Can fractional quantum Hall effect be due to the formation of coherent wave structures in a 2D electron gas?

2016 ◽  
Vol 30 (13) ◽  
pp. 1650142
Author(s):  
Babur M. Mirza
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Electron Gas ◽  
Density Wave ◽  
Quantum Hall ◽  
Microscopic Theory ◽  
Fractional Quantum Hall Effect ◽  
Hall Resistance ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

A microscopic theory of integer and fractional quantum Hall effects is presented here. In quantum density wave representation of charged particles, it is shown that, in a two-dimensional electron gas coherent structures form under the low temperature and high density conditions. With a sufficiently high applied magnetic field, the combined [Formula: see text] particle quantum density wave exhibits collective periodic oscillations. As a result the corresponding quantum Hall voltage function shows a step-wise change in multiples of the ratio [Formula: see text]. At lower temperatures further subdivisions emerge in the Hall resistance, exhibiting the fractional quantum Hall effect.

Magneto-optical evidence for fractional quantum Hall states down to filling factor 1/9

1990 ◽  
Vol 65 (8) ◽  
pp. 1056-1059 ◽  
Author(s):  
H. Buhmann ◽  
W. Joss ◽  
K. von Klitzing ◽  
I. V. Kukushkin ◽  
G. Martinez ◽  
...  
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Optical Evidence ◽  
Hall States

FRACTIONAL QUANTUM HALL EFFECT: CONSTRUCTION OF THE HARTREE–FOCK STATE BY USING TRANSLATIONAL COVARIANCE

1994 ◽  
Vol 08 (05) ◽  
pp. 529-579 ◽  
Author(s):  
R. FERRARI
Keyword(s):  
Magnetic Field ◽  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Hartree Fock

The formalism introduced in a previous paper is used for discussing the Coulomb interaction of many electrons moving in two space-dimensions in the presence of a strong magnetic field. The matrix element of the Coulomb interaction is evaluated in the new basis, whose states are invariant under discrete translations (up to a gauge transformation). This paper is devoted to the case of low filling factor, thus we limit ourselves to the lowest Landau level and to spins all oriented along the magnetic field. For the case of filling factor νf = 1/u we give an Ansatz on the state of many electrons which provides a good approximated solution of the Hartree–Fock equation. For general filling factor νf = u′/u a trial state is given which converges very rapidly to a solution of the self-consistent equation. We generalize the Hartree–Fock equation by considering some correlation: all quantum states are allowed for the u′ electrons with the same translation quantum numbers. Numerical results are given for the mean energy and the energy bands, for some values of the filling factor (νf = 1/2, 1/3, 2/3, 1/4, 3/4, 1/5, 2/5, 3/5, 4/5). Our results agree numerically with the Charge Density Wave approach. The boundary conditions are shown to be very important: only large systems (degeneracy of Landau level over 200) are not affected by the boundaries. Therefore results obtained on small scale systems are somewhat unreliable. The relevance of the results for the Fractional Quantum Hall Effect is briefly discussed.

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