Temperature dependent resistivity in the low-resistance region for diffusive transport in two dimensions

Abstract

The interpretation of the metal-insulator transition phenomena in disordered two-dimensional electron systems in terms of density-dependent scaling variables suggests the existence of a quantum critical point at some critical electron density. However a first principles scaling theory based on renormalization group (RG) methods predicts a strong temperature dependence of the dimensionless resistivity $\mathcal{R}(T)$, even at small $\mathcal{R}(T)$, that is not observed. The observed properties are in fact consistent with a weakly disordered Fermi liquid, and there are no indications of strong temperature dependence induced by scaling. While the RG expansion in a power series in $\mathcal{R}(T)$ has only been evaluated to lowest order, this should be sufficient to describe experiments in the region of very small $\mathcal{R}$. A further apparent anomaly is a return from metal-like to insulating-like behavior for increasing density. We explain these fundamental discrepancies between the first principles theory and experiment. We find that the $\mathcal{R}⪡1$ data in the currently attainable temperature range are in a weak scaling regime described by the logarithmic approximation. We independently determine the density dependent prefactor of the logarithm using data for the spin susceptibility and effective mass. We find good agreement between theory and experiment for $\mathcal{R}(T)$ in the diffusive regime. We point out that there are corrections to the leading logarithm approximation that should be observable at still lower temperatures.