Do metals exist in two dimensions? A study of many-body localisation in low density electron gas

TL;DR

This study investigates how Coulomb interactions influence electron localization in disordered two-dimensional electron gases, revealing that correlations can significantly delocalize electrons, especially with valley degeneracy, explaining metallic behavior in high mobility Si MOSFETs.

Contribution

The paper demonstrates that electron-electron interactions can delocalize 2D electrons, providing a simple mechanism for metallic behavior without true metallicity in the thermodynamic limit.

Findings

Correlations increase localization length in 2D electron gases.

Valley degeneracy enhances delocalization effects.

Results align with observed metallic behavior in Si MOSFETs.

Abstract

Using a combination of ground state quantum Monte-Carlo and finite size scaling techniques, we perform a systematic study of the effect of Coulomb interaction on the localisation length of a disordered two-dimensional electron gas. We find that correlations delocalise the 2D system. In the absence of valley degeneracy (as in GaAs heterostructures), this delocalization effect corresponds to a finite increase of the localization length. The delocalisation is much more dramatic in the presence of valley degeneracy (as in Si MOSFETSs) where the localization length increases drastically. Our results suggest that a rather simple mechanism can account for the main features of the metallic behaviour observed in high mobility Si MOSFETs. Our findings support the claim that this behaviour is indeed a genuine effect of the presence of electron-electron interactions, yet that the system is not a ``true'' metal in the thermodynamic sense.