Effect of Coulomb interaction on Anderson localization in the two-dimensional electron gas

We study the effect of Coulomb interaction on Anderson localisation in the disordered two-dimensional electron gas. Our objective is to determine wether or not there are metals in two dimensions. Without interaction, the scaling theory of localisation predicts that an arbitrarily small disorder is enough to localise the electronic wavefunction and therefore, to drive the two-dimensional system toward an insulating state at zero temperature (Abrahams et al., 1979). In some extreme limits, the interactions can be taken into account and one also finds an insulating state. However, there is no analytical tool to deal with the quantum non-perturbative regime, where both disorder and interactions are intermediate. Experimentally, it can be explored in low density and high mobility two-dimensional samples. Since 1994, unexplained metallic behaviors have been observed in this regime (Kravchenko et al., 1994). We have developed a numerical technique to study the interplay between Anderson localisation and electronic interactions. It uses a combination of ground state Quantum Monte Carlo and finite size scaling for the Thouless conductance. We find that the scaling theory of localisation is unaffected by electronic correlations, so that the two-dimensional electron gas stay in an insulating state at zero temperature. However, our results show that correlations delocalise the two-dimensional system and that the delocalisation is much more dramatic in the presence of valley degeneracy. These results suggest a simple mechanism that accounts for the main experimental features of the observed metallic phase.