Accurate prediction of macroscopic transport from microscopic imaging via critical fractals at the Mott transition

Abstract

Vanadium dioxide (VO$_2$) exhibits hysteresis in resistance while undergoing a thermally driven insulator-metal transition (IMT). Understanding the nonequilibrium effects in resistance is of great interest, as VO$_2$ is a strong candidate for brain-inspired computing, which is more energy efficient for AI tasks compared to traditional computing. Accurate models of the connection between microscopic and macroscopic transport properties and microscopic imaging of VO$_2$ will allow us to better utilize VO$_2$ in future applications. However, predictions of macroscopic resistance of VO$_2$ that quantitatively match observations using spatially resolved data have not yet been achieved. Here, we demonstrate an accurate prediction of the macroscopic resistance of VO$_2$ throughout the entire temperature range of interest, by developing a multiscale resistor network model incorporating the assumption of fractal sub-pixel structure of the optical data, where the configuration of insulating and metallic domains within each pixel are drawn from the random field Ising model near criticality. This strongly indicates that the observed fractal, power law structure of metallic and insulating domains extends down to much smaller length scales than the current record for experimental resolution of this system, and that the two-dimensional random field Ising model near criticality is a suitable model for describing the metal and insulator patches of VO$_2$ down to scales that approach the unit cell.