Low Temperature Properties of 2D Correlated Electrons in Weakly Disordered Materials

Transport properties of extremely high purity two-dimensional (2D) electron systems at low temperatures are still not well understood either experimentally or theoretically, even though these systems are fast becoming a mainstream basis of computing devices. In fact there are two separate issues to be resolved. The first of these has attracted the more attention. This is the existence of a quantum phase transition (the metal-insulator transition) in the low density 2D system at zero temperature. Experimentally, in spite of claims, from existing data at finite temperatures there is no conclusive evidence either way on the existence of a T = 0 quantum phase transition. There is a need for a unified theory encompassing, on the same level, both insulating and metallic behaviour to predict the cross-over. We propose a semi-empirical one parameter renormalisation group equation for the temperature dependent resistivity of a 2D electron system with weak disorder. The renormalisation group equation has a physically meaningful insulating limit and it predicts a metallic ground state of zero resistance at higher electron densities. The resulting temperature dependence of the resistivity is found to give a good fit to experimental data near the separatrix. The second issue is the mechanism behind the sudden change in the temperature dependence of the resistivity, as is actually observed at low but non-zero temperatures, T = 0.1 to 2 K. This phenomenon is well-documented experimentally and it is of interest in its own right whether or not there is an actual transition at T = 0. We present direct evidence of the important role of the electron Coulomb repulsion and exchange in determining these finite temperature properties by noting an empirical relationship between the critical density at the bifurcation point and parallel magnetic field. The relationship is controlled by properties of the electron-electron correlation function for the 2D electron system. This result provides direct evidence of the central role of the Coulomb repulsion and exchange in driving the bifurcation phenomenon.