Two-Component Scaling near the Metal-Insulator Bifurcation in Two-Dimensions

TL;DR

This paper develops a two-component scaling framework to describe the resistivity behavior of two-dimensional disordered electron systems near the metal-insulator transition, successfully fitting experimental data and discussing quantum criticality implications.

Contribution

It introduces a semi-empirical two-component scaling theory that captures bifurcation behavior in 2D electron systems, extending beyond conventional renormalization group approaches.

Findings

Excellent fit to silicon resistance data near the separatrix.

Parameters like zν are determined through least squares fitting.

Discusses implications for quantum critical points.

Abstract

We consider a two-component scaling picture for the resistivity of two-dimensional (2D) weakly disordered interacting electron systems at low temperature with the aim of describing both the vicinity of the bifurcation and the low resistance metallic regime in the same framework. We contrast the essential features of one-component and two-component scaling theories. We discuss why the conventional lowest order renormalization group equations do not show a bifurcation in 2D, and a semi-empirical extension is proposed which does lead to bifurcation. Parameters, including the product $z\nu$, are determined by least squares fitting to experimental data. An excellent description is obtained for the temperature and density dependence of the resistance of silicon close to the separatrix. Implications of this two-component scaling picture for a quantum critical point are discussed.