Quantifying disorder using a simple model for electrical transport in inhomogeneous 2D superconductors

Disorder in 2D materials can dramatically affect the transition into superconducting phases, such as creating a large transverse voltage response near T_c even in the absence of a magnetic field. We extend the model of disordered conductors by Parish and Littlewood (Nature 426, 162 (2003)) to granular superconducting materials by adding a site-dependent critical temperature that can be correlated with the local resistivity. Using this model, we are able to visualize the onset of global superconductivity and accompanying changes in material resistivity and patterns of current flow under randomly-distributed degrees of material disorder at different length scales. We also explore the variance in longitudinal and transverse resistance at different disorder scales. Our results provide a framework for quantifying the level of disorder using experimentally reported magnetoresistance and transverse voltage measurements.