Origin of the quasi-universality of the graphene minimal conductivity

It is a fact that the minimal conductivity ${\sigma }_0$ of most graphene samples is larger than the well-established universal value for ideal graphene $4e^2\mathrm{/}\pi h$; in particular, larger by a factor $\gtrsim \pi$. Despite intense theoretical activity, this fundamental issue has eluded an explanation so far. Here we present fully atomistic quantum mechanical estimates of the graphene minimal conductivity where electron-electron interactions are considered in the framework of density functional theory. We show the first conclusive evidence of the dominant role on the minimal conductivity of charged impurities over ripples, which have no visible effect. Furthermore, in combination with the logarithmic scaling law for diffusive metallic graphene, we ellucidate the origin of the ubiquitously observed minimal conductivity in the range $8e^2/h > \sigma_0 \gtrsim 4e^2/h$.