TITLE:
Fractional Quantum Hall States for Filling Factors 2/3 ν
AUTHORS:
Shosuke Sasaki
KEYWORDS:
Fractional Quantum Hall Effect, 2D Electron System, Quantum Theory
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.5,
April
10,
2015
ABSTRACT: Fractional quantum Hall effect (FQHE) is investigated by employing
normal electrons and the fundamental Hamiltonian without any quasi particle.
There are various kinds of electron configurations in the Landau orbitals.
Therein only one configuration has the minimum energy for the sum of the Landau
energy, classical Coulomb energy and Zeeman energy at any fractional filling
factor. When the strong magnetic field is applied to be upward, the Zeeman
energy of down-spin is lower than that of up-spin for electrons. So, all the
Landau orbitals in the lowest level are occupied by the electrons with
down-spin in a strong magnetic field at 1 ν . On the other hand, the Landau
orbitals are partially occupied by up-spins. Two electrons with up-spin placed
in the nearest orbitals can transfer to all the empty orbitals of up-spin at
the specific filling factors and so on. When the
filling factor ν deviates from ν0, the number of allowed transitions
decreases abruptly in comparison with that at ν0. This mechanism creates the energy
gaps at ν0. These energy gaps yield the
fractional quantum Hall effect. We compare the present theory with the
composite fermion theory in the region of 2/3 ν .