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>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 1/2tau does not exceed the critical value 1/2tau(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)much less than1 and therefore can be neglected.