Mean-field Phase Diagram of Two-Dimensional Electrons with Disorder in a Weak Magnetic Field

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $\nu \gg 1$ and in the presence of a quenched disorder. In the framework of the Hartree-Fock approximation, we obtain the mean-field phase diagram for the partially filled highest Landau level. We find that the CDW state can exist if the Landau level broadening $1\mathrm{/}2\tau$ does not exceed the critical value $1\mathrm{/}2{\tau }_c=0.038{\omega }_H$. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1\mathrm{/}\nu {)}^{2\mathrm{/}3}\ll 1$ and therefore can be neglected.