TITLE:
Spin Polarization of Fractional Quantum Hall States with ν
AUTHORS:
Shosuke Sasaki
KEYWORDS:
Spin Polarization, Fractional Quantum Hall Effect, 2D Electron System, Quantum Theory
JOURNAL NAME:
Journal of Modern Physics,
Vol.6 No.6,
May
25,
2015
ABSTRACT: The spin polarization of a fractional quantum Hall state shows very
interesting properties. The curve of polarization versus magnetic field has
wide plateaus. The fractional quantum Hall effect is caused by the Coulomb
interaction because the 2D electron system without the Coulomb interaction yields
no energy gap at the fractional filling factor. Therefore, the wide plateau in
the polarization curve is also caused by the Coulomb interaction. When the
magnetic field is weak, some electrons have up-spins and the others down-spins.
Therein the spin-exchange transition occurs between two electrons with up and
down spins via the Coulomb interaction. Then the charge distribution before the
transition is the same as one after the transition. So these two states have
the same classical Coulomb energy. Accordingly, the partial Hamiltonian
composed of the spin exchange interaction should be treated exactly. We have
succeeded in diagonalizing the spin exchange interaction for the first and
second nearest electron pairs. The theoretical results reproduce the wide
plateaus very well. If the interval modulations between Landau orbitals are
taken into the Hamiltonian, the total energy has the Peierls instability. We
can diagonalize the Hamiltonian with the interval modulation. The results
reproduce wide plateaus and small shoulders which are in good agreement with
the experimental data.