Table of Contents
ISRN Condensed Matter Physics
Volume 2013, Article ID 489519, 19 pages
Research Article

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

Center for Quantum Science and Technology under Extreme Conditions (KYOKUGEN), Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

Received 30 June 2013; Accepted 12 August 2013

Academic Editors: H. Hibino and A. N. Kocharian

Copyright © 2013 Shosuke Sasaki. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.