Based on the recently developed picture of an electronic ideal relativistic
fluid at the Dirac point, we present an analytical model for the conductivity
in graphene that is able to describe the linear dependence on the carrier
density and the existence of a minimum conductivity. The model treats
impurities as submerged rigid obstacles, forming a disordered medium through
which graphene electrons flow, in close analogy with classical fluid dynamics.
To describe the minimum conductivity, we take into account the additional
carrier density induced by the impurities in the sample. The model, which
predicts the conductivity as a function of the impurity fraction of the sample,
is supported by extensive simulations for different values of E, the
dimensionless strength of the electric field, and provides excellent agreement
with experimental data.Comment: 19 pages, 4 figure
