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

Abstract

We study two-dimensional interacting electrons in a weak perpendicular magnetic field with the filling factor $ν\gg 1$ 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 $1/2τ$ does not exceed the critical value $1/2τ_{c}=0.038ω_{H}$. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1/ν)^{2/3}\ll 1$ and therefore can be neglected.