  Pristine graphene and graphene-based heterostructures exhibit exceptionally
high electron mobility and conductance if their surface contains few
electron-scattering impurities. Here, we reveal a universal connection between
graphene's carrier mobility and the variation of its electrical conductance
with carrier density. Our model of graphene conductivity is based on a
convolution of carrier density and its uncertainty, which reproduces the
observed universality. Taking a single conductance measurement as input, this
model accurately predicts the full shape of the conductance versus carrier
density curves for a wide range of reported graphene samples. We verify the
convolution model by numerically solving the Boltzmann transport equation to
analyse in detail the effects of charged impurity scattering on carrier
mobility. In this model, we also include optical phonons, which relax
high-energy charge carriers for small impurity densities. Our numerical and
analytical results both capture the universality observed in experiment and
provide a way to estimate all key transport parameters of graphene devices. Our
results demonstrate how the carrier mobility can be predicted and controlled,
thereby providing insights for engineering the properties of 2D materials and
heterostructures.
