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

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

scholarly journals FRACTIONAL QUANTUM HALL STATES WITH NEGATIVE FLUX: EDGE MODES IN SOME ABELIAN AND NON-ABELIAN CASES

2010 ◽  
Vol 24 (05) ◽  
pp. 549-566 ◽  
Author(s):  
M. V. MILOVANOVIĆ ◽  
TH. JOLICOEUR
Keyword(s):  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Singlet States ◽  
Spin Singlet ◽  
Spin Polarized ◽  
Negative Flux ◽  
Hall States

We investigate the structure of gapless edge modes propagating at the boundary of some fractional quantum Hall states. We show how to deduce explicit trial wavefunctions from the knowledge of the effective theory governing the edge modes. In general, quantum Hall states have many edge states. Here, we discuss the case of fractions having only two such modes. The case of spin-polarized and spin-singlet states at filling fraction ν = 2/5 is considered. We give an explicit description of the decoupled charged and neutral modes. Then we discuss the situation involving negative flux acting on the composite fermions. This happens notably for the filling factor ν = 2/3 which supports two counterpropagating modes. Microscopic wavefunctions for spin-polarized and spin-singlet states at this filling factor are given. Finally, we present an analysis of the edge structure of a non-Abelian state involving also negative flux. Counterpropagating modes involve, in all cases, explicit derivative operators diminishing the angular momentum of the system.

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

2013 ◽  
Vol 2013 ◽  
pp. 1-19 ◽  
Author(s):  
Shosuke Sasaki
Keyword(s):  
Magnetic Field ◽  
Spin Polarization ◽  
Filling Factor ◽  
Minimum Energy ◽  
Quantum Hall ◽  
Ground States ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Hall States

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 down-spins. 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.

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