Effect of electron-electron interaction and disorder potential on the localization of two-dimensional electrons in a strong magnetic field

The density functional theory is used to study the electronic structure of a quantum wire in a magnetic field. The Kohn-Sham equations are solved numerically for different values of electron densities and filling factors. The critical density, below which the electron density has a strong spatial inhomogeneity, was found in GaAs quantum wire. An empirical formula for the critical density is obtained. The effect of the disorder potential on the electron density profile in a two-dimensional electron gas is estimated.