scholarly journals COULOMB GAP IN THE QUANTUM HALL INSULATOR

2001 ◽  
Vol 15 (10n11) ◽  
pp. 1369-1372 ◽  
Author(s):  
MICHAEL BACKHAUS ◽  
BODO HUCKESTEIN
Keyword(s):  
Filling Factor ◽  
Particle Density ◽  
Quantum Hall ◽  
Correct Treatment ◽  
Coulomb Gap ◽  
Hartree Fock ◽  
Strong Disorder ◽  
Single Particle Density ◽  
Lowest Landau Level ◽  
Classical Point

We calculate numerically the spectrum of disordered electrons in the lowest Landau level at filling factor 1/5 using the self-consistent Hartree-Fock approximation for systems containing up to 400 flux quanta. Special attention is paid to the correct treatment of the q=0 component of the Coulomb interaction. For sufficiently strong disorder, the system is an insulator at this filling factor. We observe numerically a Coulomb gap in the single-particle density of states (DOS). The DOS agrees quantitatively with the predictions for classical point charges.

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.

SKYRMIONS IN QUANTUM HALL FERROMAGNETS

1999 ◽  
Vol 13 (05n06) ◽  
pp. 461-468 ◽  
Author(s):  
H. A. FERTIG
Keyword(s):  
Close Agreement ◽  
Filling Factor ◽  
Quantum Hall ◽  
Time Dependent ◽  
Square Lattice ◽  
Hartree Fock ◽  
Quantum Hall Systems ◽  
Spin Ordering ◽  
Lattice State ◽  
The Stability

Properties of skyrmions in quantum Hall systems are reviewed. It is shown that, using a Hartree-Fock technique, the size of skyrmions near filling factor ν=1 may be computed, yielding a result in close agreement with experiment. Finite densities of skyrmions are shown to lead to a crystal state with square symmetry due to the spin-dependent nature of their mutual interactions. The square lattice state has an unusual spin ordering which leads to a new gapless mode, analogous to spin waves in a two-dimensional XY antiferromagnet. The stability of the ordered spin state is assessed using a time-dependent Hartree-Fock approach, and a phase diagram is derived which shows the parameter range for which long-range spin ordering is destroyed by quantum fluctuations.

ONE-PARTICLE DENSITY OF LAUGHLIN STATES AT FINITE N

2011 ◽  
Vol 25 (25) ◽  
pp. 1983-1992 ◽  
Author(s):  
ORION CIFTJA ◽  
NICOLE OCKLEBERRY ◽  
CHIKO OKOLO
Keyword(s):  
Particle Density ◽  
Quantum Hall ◽  
Electronic Systems ◽  
Strongly Correlated ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Strongly Correlated Electronic Systems ◽  
Lowest Landau Level ◽  
Laughlin States ◽  
The One

The most robust fractional quantum Hall states occur in the lowest Landau level at filling factors, 1/3 and 1/5. Such states are very well described by Laughlin's wave function. In this work, we have succeeded in calculating exactly the one-particle density function of the Laughlin states for some finite systems of particles in a disk geometry. The exact results we provide are not only important for the Laughlin states, but also for the general field of numerical calculations because they can serve as benchmarks to test the accuracy of various approaches, numerical schemes and computational methods used in studies of strongly correlated electronic systems.

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

The role of single-particle density in chemistry

1981 ◽  
Vol 53 (1) ◽  
pp. 95-126 ◽  
Author(s):  
Anjuli S. Bamzai ◽  
B. M. Deb
Keyword(s):  
Single Particle ◽  
Particle Density ◽  
Single Particle Density

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.

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