Modelling the minimum conductivity of graphene using random resistor networks

In this paper, we propose a model of random resistor networks that describes monolayer graphene sheets. We investigate the conductivity behaviour of these networks in two scenarios, depending on the distribution of either charge puddles, which are local accumulations of charge carriers, or contacts between negative (n) and positive (p) puddles. In both scenarios, we observed a minimum conductivity behaviour at a certain proportion p=p0 of the puddles and their contacts. In the contacts’ distribution scenario, the conductivity demonstrated a linear relationship around p0 without any finite-size effects. In contrast, in the puddles’ scenario, no such linearity was observed, indicating that the conductivity behaviour is influenced by the degree of inhomogeneity. The results demonstrate a power-law emergent response for the global conductivity versus the conductances’ ratio γ=σp−n/σp−p=σp−n/σn−n, where σn−n, σp−p and σp−n are the conductivity of n-n, p-p and p-n junctions, respectively.