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 $T\tau >1$ or $\mu \tau >1$, where $\tau$ is the scattering time and $\mu$ the chemical potential. At the critical value of the chemical potential, the resistivity diverges as a power law, $R_c\sim 1\mathrm{/}T$. Consequently, on the metallic side there is a regime with negative $dR\mathrm{/}dT$, which is often misinterpreted as insulating. We show that scaling and this `fake insulator’ regime is observed in a wide range of experimental systems. In particular, we show that Mooij correlations in high-temperature metals with negative $dR\mathrm{/}dT$ can be quantitatively understood with our scaling theory in the presence of $T$-linear scattering.