Flow diagram of the metal-insulator transition in two dimensions

TL;DR

This paper investigates the metal-insulator transition in two-dimensional electron systems, demonstrating a quantum critical point and confirming theoretical predictions through experimental measurements of resistance and interactions.

Contribution

It provides the first experimental resistance-interaction flow diagram of the 2D MIT, confirming the two-parameter scaling theory and identifying a quantum critical point.

Findings

Identification of a quantum critical point at the MIT

Experimental validation of the renormalization group theory predictions

Resistance temperature dependence aligns with theoretical interaction amplitude

Abstract

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems challenged the veracity of one of the most influential conjectures in the physics of disordered electrons, which states that `in two dimensions, there is no true metallic behaviour'; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory (Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this diagram is accurately described by the renormalization group theory without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a value in remarkable agreement with the one predicted by the theory.