Continuum excitons in the fractional-quantum-Hall-effect regime: Steps in the filling-factor dependence of the energy

1994 ◽  
Vol 50 (23) ◽  
pp. 17349-17356 ◽  
Author(s):  
T. V. Tatarinova ◽  
E. I. Rashba ◽  
A. L. Efros
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

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.

scholarly journals Filling Factor Dependence of the Fractional Quantum Hall Effect Gap

2008 ◽  
Vol 100 (19) ◽  
Author(s):  
V. S. Khrapai ◽  
A. A. Shashkin ◽  
M. G. Trokina ◽  
V. T. Dolgopolov ◽  
V. Pellegrini ◽  
...  
Keyword(s):  
Hall Effect ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

SPIN-ORBIT COUPLING OF TWO-DIMENSIONAL ELECTRONS AND LANDAU LEVELS FILLING FACTOR IN FRACTIONAL QUANTUM HALL EFFECT

2021 ◽  
Vol 77 ◽  
pp. 130-140
Author(s):  
A. A. Kornilovich ◽  
◽  
V. G. Litvinov ◽  
Keyword(s):  
Hall Effect ◽  
Landau Level ◽  
Quantum Hall Effect ◽  
Filling Factor ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Contactless Method ◽  
Two Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall

A mechanism for pairing and joining two-dimensional electron clusters in a strong quantizing magnetic field is proposed. The aim of this work is to obtain the dependence of the filling factor on the Landau level number N the resulting spin S and magnetic mL quantum numbers determined by the L-S bond of twodimensional electrons. A contactless method for determining the Landau level filling factor  has been developed. An interpretation of the fractional quantum Hall effect is given.

Second Activation Energy in the Fractional Quantum Hall Effect

1987 ◽  
Vol 56 (9) ◽  
pp. 3005-3008 ◽  
Author(s):  
Junichi Wakabayashi ◽  
Satoru Sudou ◽  
Shinji Kawaji ◽  
Kazuhiko Hirakawa ◽  
Hiroyuki Sakaki
Keyword(s):  
Activation Energy ◽  
Hall Effect ◽  
Quantum Hall Effect ◽  
Quantum Hall ◽  
Fractional Quantum Hall Effect ◽  
Fractional Quantum ◽  
Fractional Quantum Hall
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