Table of Contents
ISRN Condensed Matter Physics
Volume 2014 (2014), Article ID 468130, 16 pages
Research Article

Plateaus in the Hall Resistance Curve at Filling Factors

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

Received 15 October 2013; Accepted 11 November 2013; Published 19 February 2014

Academic Editors: S. Bud'ko, H. Eisaki, and V. Gasparian

Copyright © 2014 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.


The fractional quantum Hall (FQH) states with higher Landau levels have new characters different from those with . The FQH states at are examined by developing the Tao-Thouless theory. We can find a unique configuration of electrons with the minimum Coulomb energy in the Landau orbitals. Therein the electron (or hole) pairs placed in the first and second nearest Landau orbitals can transfer to all the empty (or filled) orbitals at , 14/5, 7/3, 11/5, and 5/2 via the Coulomb interaction. More distant electron (or hole) pairs with the same centre position have the same total momentum. Therefore, these pairs can also transfer to all the empty (or filled) orbitals. The sum of the pair energies from these quantum transitions yields a minimum at . The spectrum of the pair energy takes the lowest value at and a higher value with a gap in the neighbourhood of because many transitions are forbidden at a deviated filling factor from . From the theoretical result, the FQH states with are stable and the plateaus appear at the specific filling factors .