The Absence of the Fractional Quantum Hall Effect at High Landau Levels

Abstract

We compare the energies of the Laughlin liquid and a charge density wave in a weak magnetic field for the upper Landau level filling factors ${\nu }_N=1/3$ and $1/5$. The charge density wave period has been optimized and was found to be $\simeq 3R_c$, where $R_c$ is the cyclotron radius. We conclude that the optimal charge density wave is more energetically preferable than the Laughlin liquid for the Landau level numbers $N\ge 2$ at ${\nu }_N=1/3$ and for $N\ge 3$ at ${\nu }_N=1/5$. This implies that the $1/3$ fractional quantum Hall effect cannot be observed for $N\ge 2$, in agreement with the experiment.

12 pages, revtex, 2 PostScript figures are applied. Revised and corrected version. Also available at http://www.mnhep.umn.edu/~mfogler/