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

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We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor ν≫ 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 1/2τ does not exceed the critical value 1/2τc=0.038ωₕ. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of (1/ν)²/³≪ 1 and therefore can be neglected.