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

TL;DR

This paper investigates the phase diagram of two-dimensional electrons with disorder in a weak magnetic field, revealing conditions for charge density wave formation and showing that weak crystallization corrections are negligible.

Contribution

It provides the first mean-field phase diagram for electrons in a disordered 2D system at high Landau levels using Hartree-Fock approximation.

Findings

CDW state exists if Landau level broadening is below a critical value

Weak crystallization corrections are negligible at large filling factors

Critical broadening value is proportional to the cyclotron frequency

Abstract

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 $1/2\tau $ does not exceed the critical value $1/2\tau_{c}=0.038\omega_{H}$. Our analysis of weak crystallization corrections to the mean-field results shows that these corrections are of the order of $(1/\nu)^{2/3}\ll 1$ and therefore can be neglected.