Flow diagram of the metal-insulator transition in two dimensions

The discovery of the metal–insulator transition (MIT) in two-dimensional electron systems1 challenged the veracity of one of the most influential conjectures2 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 theory3. The metallic side of this diagram is accurately described by the renormalization-group theory4 without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches γ2≈0.45—a value in remarkable agreement with the one predicted by theory4.