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 charge-density-wave (CDW) state can exist if the Landau level broadening $1/2\tau$ does not exceed the critical value $1/2{\tau }_c{=4T}_0/\pi ,$ where $T_0$ is the critical temperature of the CDW formation in the clean case. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1/\nu {)}^{2/3}\ll 1$ and therefore can be neglected.