Laughlin liquid to charge-density-wave transition at high Landau levels

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 ${\nu }_{\mathrm{N}}$= and . The charge-density-wave period has been optimized and was found to be ≃3.${3\mathrm{R}}_{\mathrm{c}}$, where ${\mathrm{R}}_{\mathrm{c}}$ is the cyclotron radius. We conclude that the optimal charge density wave is lower in energy than the Laughlin liquid for the Landau-level numbers N⩾2 at ${\nu }_{\mathrm{N}}$= and for N⩾3 at ${\nu }_{\mathrm{N}}$=. This implies that the quantum Hall plateaus cannot be observed for N⩾2, in agreement with the experiment.