Flow diagram of the metal-insulator transition in two dimensions

The discovery of the metal-insulator transition (MIT) in two-dimensional electron systems(1) challenged the veracity of one of the most influential conjectures(2) 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(3). The metallic side of this diagram is accurately described by the renormalization-group theory(4) without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches gamma(2) approximate to 0.45 - a value in remarkable agreement with the one predicted by theory(4).