Universal Scaling near Band-Tuned Metal-Insulator Phase Transitions

We present a theory for band-tuned metal-insulator transitions based on the Kubo formalism. Such a transition exhibits scaling of the resistivity curves in the regime where 𝑇⁢𝜏 >1 or 𝜇⁢𝜏 >1, where 𝜏 is the scattering time and 𝜇 the chemical potential. At the critical value of the chemical potential, the resistivity diverges as a power law, 𝑅𝑐∼1/𝑇. Consequently, on the metallic side there is a regime with negative 𝑑⁢𝑅/𝑑⁢𝑇, which is often misinterpreted as insulating. We show that scaling and this “fake insulator” regime are observed in a wide range of experimental systems. In particular, we show that Mooij correlations in high-temperature metals with negative 𝑑⁢𝑅/𝑑⁢𝑇 can be quantitatively understood with our scaling theory in the presence of 𝑇-linear scattering.