Density functional calculations may shine some light on the interplay between disorder and interactions:

Recent experiments in Si inversion layers and GaAs-AlGaAs interfaces have revealed appearance of magnetism as well as a metal to insulator transition (MIT) as the density is lowered.

We are investigating these phenomena by using the density functional theory and a recent parametrization of the exchange-correlation potential by Attaccalite et al. In these systems both disorder and electron correlations play an important role. The strength of disorder is defined by the dopant concentration and their distance from the electron layer. Correlations, however, depend on the electron density, itself controlled via an applied gate voltage. At high densities the behavior of the system can be described by the Fermi liquid theory. The electron gas behaves as a metal since its low-temperature resistance goes up with temperature.

 

 

 

 

 

 

 

At these densities electrons screen the disorder effectively so that the effective potential seen by them is much more smooth. As the density is lowered, charge depletion takes place, the screening becomes non-linear and potential landscape rough. It was found that at the onset of charge depletion the magnetic susceptibility becomes maximum. For even lower densities percolation transition occurs where we have also observed a minimum in the inverse compressibility. Electron puddles start forming due to the presence of strong disorder.

In regions of very low density, one can find spin-polarization with high magnetic susceptibility. At very low densities the system goes to the Wigner Crystal phase if disorder is weak, or to an insulating glassy phase where electrons are localized by the strong disorder. In this regime the resistance decreases as the temperature goes up. The transition between the two regimes where the behavior of resistivity with T changes is identified with the MIT. One question we are addressing is the relationship between the MIT point and anomalies seen in the thermodynamic properties such as magnetic susceptibility and inverse compressibility.

A Hypothetical phase diagram

Profile of the unscreened disorder potential due to remote ionized impurities displayed on a 128x128 mesh. At low densities valleys are filled with electrons which screen them. This makes the dips smoother, whereas hills will still have large fluctuations. At high densities screening becomes linear.